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Deck 8: Topics in Analytic Geometry
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Question
Find the vertex, focus, and directrix of the parabola given by the equation. 
A)vertex:
, focus: 
, directrix: 
B)vertex:
, focus: 
, directrix: 
C)vertex:
, focus: 
, directrix: 
D)vertex:
, focus: 
, directrix: 
E)vertex:
, focus: 
, directrix: 
A)vertex:
, focus: , directrix: B)vertex:
, focus: , directrix: C)vertex:
, focus: , directrix: D)vertex:
, focus: , directrix: E)vertex:
, focus: , directrix: 
Question
Question
By using the definition of a parabola, find the equation in standard form of the parabola with V (0, 0), F ( s , 0), and directrix 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
The line segment that has endpoints on a parabola, passes through the focus of the parabola, and is perpendicular to the axis of symmetry is called the latus rectum of the parabola. 
Find the length of the latus rectum for the parabola 
.
A)152
B)38
C)76
D)57
E)19
Find the length of the latus rectum for the parabola .A)152
B)38
C)76
D)57
E)19
Question
Find the equation in standard form of the parabola that has vertex 
, has a horizontal axis of symmetry, and passes through the point 
.
A)
B)
C)
D)
E)
, has a horizontal axis of symmetry, and passes through the point .A)
B)
C)
D)
E)
Question
Find the vertex, focus, and directrix of the parabola given by the equation. 
A)vertex: (0, -3), focus: (0, 0), directrix: y = 3
B)vertex: (0, 0), focus: (0, 3), directrix: y = -3
C)vertex: (0, 0), focus: (0, -3), directrix: y = 3
D)vertex: (0, 0), focus: (0, -12), directrix: y = 12
E)vertex: (0, -3), focus: (0, 3), directrix: y = 0
A)vertex: (0, -3), focus: (0, 0), directrix: y = 3
B)vertex: (0, 0), focus: (0, 3), directrix: y = -3
C)vertex: (0, 0), focus: (0, -3), directrix: y = 3
D)vertex: (0, 0), focus: (0, -12), directrix: y = 12
E)vertex: (0, -3), focus: (0, 3), directrix: y = 0
Question
Graph the equation below. 
= 
A)
B)
C)
D)
E)
= A)
B)
C)
D)
E)
Question
Graph the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The surface area of a paraboloid with radius r and depth d is given by 
. The antenna of a radio telescope is a paraboloid measuring 89 feet across with a depth of 18 feet. Approximate (to the nearest 100 square feet)the surface area of the radio telescope.
A)13,300 ft2
B)7100 ft2
C)1600 ft2
D)25,900 ft2
E)7600 ft2
. The antenna of a radio telescope is a paraboloid measuring 89 feet across with a depth of 18 feet. Approximate (to the nearest 100 square feet)the surface area of the radio telescope.A)13,300 ft2
B)7100 ft2
C)1600 ft2
D)25,900 ft2
E)7600 ft2
Question
Graph the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the equation in standard form of the parabola with vertex at 
and focus 
.
A)
B)
C)
D)
E)
and focus .A)
B)
C)
D)
E)
Question
Find the vertex, focus, and directrix of the parabola given by the equation. 
A)vertex :
, focus : 
, directrix : 
B)vertex :
, focus : 
, directrix : 
C)vertex :
, focus : 
, directrix : 
D)vertex :
, focus : 
, directrix : 
E)vertex :
, focus : 
, directrix : 
A)vertex :
, focus : , directrix : B)vertex :
, focus : , directrix : C)vertex :
, focus : , directrix : D)vertex :
, focus : , directrix : E)vertex :
, focus : , directrix : Question
Find the vertex of the parabola given by the equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
The line segment that has endpoints on a parabola, passes through the focus of the parabola, and is perpendicular to the axis of symmetry is called the latus rectum of the parabola. 
Find the length of the latus rectum for the parabola 
.
A)24
B)12
C)36
D)48
E)96
Find the length of the latus rectum for the parabola .A)24
B)12
C)36
D)48
E)96
Question
The Lovell Telescope is a radio telescope located at the Jodrell Bank Observatory in Cheshire, England. The dish of the telescope has the shape of a paraboloid with a diameter of 240 feet. The distance from the vertex of the dish to its focus is 85 feet. The surface area of a paraboloid with radius r and depth d is given by 
. Approximate (to the nearest 100 square feet)the surface area of the radio telescope.
A)118,900 ft2
B)63,300 ft2
C)50,500 ft2
D)186,500 ft2
E)50,500 ft2.
. Approximate (to the nearest 100 square feet)the surface area of the radio telescope.A)118,900 ft2
B)63,300 ft2
C)50,500 ft2
D)186,500 ft2
E)50,500 ft2.
Question
Ultrasound is used as a nondestructive method of determining whether a support beam for a structure has an internal fracture. In one scanning procedure, if the resulting image is a parabola, engineers know that there is a structural defect. Suppose that a scan produced an image whose equation is 
. Determine the vertex and focus of the graph of this parabola.
A)vertex:
, focus: 
B)vertex:
, focus: 
C)vertex:
, focus: 
D)vertex:
, focus: 
E)vertex:
, focus: 
. Determine the vertex and focus of the graph of this parabola.A)vertex:
, focus: B)vertex:
, focus: C)vertex:
, focus: D)vertex:
, focus: E)vertex:
, focus: Question
Question
Find the equation in standard form of the parabola with focus 
and directrix 
.
A)
B)
C)
D)
E)
and directrix .A)
B)
C)
D)
E)
Question
A fountain in a shopping mall has two parabolic arcs of water intersecting as shown below. The equation of one parabola is 
and the equation of the second parabola is 
. 
How high above the base of the fountain do the parabolas intersect? All dimensions are in feet. Round your answer to the nearest hundredth.
A)5.91 feet
B)6.40 feet
C)2.95 feet
D)3.45 feet
E)8.86 feet
and the equation of the second parabola is . How high above the base of the fountain do the parabolas intersect? All dimensions are in feet. Round your answer to the nearest hundredth.A)5.91 feet
B)6.40 feet
C)2.95 feet
D)3.45 feet
E)8.86 feet
Question
Find the equation in standard form of the parabola with vertex at 
and focus 
.
A)
B)
C)
D)
E)
and focus .A)
B)
C)
D)
E)
Question
Find the center, vertices, and foci of the ellipse given by the equation. 
A)center:
, vertices: 
, foci: 
B)center:
, vertices: 
, foci: 
C)center:
, vertices: 
, foci: 
D)center:
, vertices: 
, foci: 
E)center:
, vertices: 
, foci: 
A)center:
, vertices: , foci: B)center:
, vertices: , foci: C)center:
, vertices: , foci: D)center:
, vertices: , foci: E)center:
, vertices: , foci: Question
Find the center of the ellipse given by the equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the equation in standard form of the ellipse, given the information provided. vertices 
, foci at 
A)
B)
C)
D)
E)
, foci at A)
B)
C)
D)
E)
Question
Use the eccentricity of the ellipse to find its equation in standard form. eccentricity 
, major axis of length 28 on the y -axis, center at (0, 0)
A)
B)
C)
D)
E)
, major axis of length 28 on the y -axis, center at (0, 0)A)
B)
C)
D)
E)
Question
A circular vent pipe with a diameter of 6.5 inches is placed on a roof that has a slope of 
as shown in the figure below. 
Use the slope to find the value of h . Round to the nearest hundredths.
A)2.44 inches
B)17.33 inches
C)4.88 inches
D)4.33 inches
E)9.75 inches
as shown in the figure below. Use the slope to find the value of h . Round to the nearest hundredths.A)2.44 inches
B)17.33 inches
C)4.88 inches
D)4.33 inches
E)9.75 inches
Question
Find the center, vertices, and foci of the ellipse given by the equation. 
A)center:
, vertices: 
, foci: 
B)center:
, vertices: 
, foci: 
C)center:
, vertices: 
, foci: 
D)center:
, vertices: 
, foci: 
E)center:
, vertices: 
, foci: 
A)center:
, vertices: , foci: B)center:
, vertices: , foci: C)center:
, vertices: , foci: D)center:
, vertices: , foci: E)center:
, vertices: , foci: Question
Find the vertices and foci of the ellipse given by the equation. 
A)vertices:
B)vertices:
C)vertices:
D)vertices:
E)vertices:
A)vertices:
B)vertices:
C)vertices:
D)vertices:
E)vertices:
Question
Use the eccentricity of the ellipse to find its equation in standard form. eccentricity 
, foci at 
A)
B)
C)
D)
E)
, foci at A)
B)
C)
D)
E)
Question
Find the equation in standard form of the ellipse, given the information provided. major axis of length 20, center at 
; ellipse passes through 
A)
B)
C)
D)
E)
; ellipse passes through A)
B)
C)
D)
E)
Question
Graph the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the equation in standard form of the ellipse with center (8, 5), minor axis parallel to the x -axis and of length 6, and that passes through point (9.5, 11).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Graph the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the equation in standard form of an ellipse with eccentricity 
, center at (0, 0), and major axis on the x -axis and of length 14.
A)
B)
C)
D)
E)
, center at (0, 0), and major axis on the x -axis and of length 14.A)
B)
C)
D)
E)
Question
Find the equation in standard form of an ellipse with center at (0, 0)minor axis of length 24, and foci at (0, -16)and (0, 16).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the equation in standard form of the ellipse, given the information provided. center 
, vertices 
, foci at 
A)
B)
C)
D)
E)
, vertices , foci at A)
B)
C)
D)
E)
Question
Find the vertices and foci of the ellipse given by the equation. 
A)vertices:
, foci: 
B)vertices:
, foci: 
C)vertices:
, foci: 
D)vertices:
, foci: 
E)vertices:
, foci: 
A)vertices:
, foci: B)vertices:
, foci: C)vertices:
, foci: D)vertices:
, foci: E)vertices:
, foci: Question
Use the eccentricity of the ellipse to find its equation in standard form. eccentricity 
, major axis of length 18 on the x -axis, center at 
A)
B)
C)
D)
E)
, major axis of length 18 on the x -axis, center at A)
B)
C)
D)
E)
Question
Use the eccentricity of the ellipse to find its equation in standard form. foci at 
, eccentricity 
A)
B)
C)
D)
E)
, eccentricity A)
B)
C)
D)
E)
Question
Find the center, vertices, and foci of the ellipse given by the equation. 
A)center:
, vertices: 
, foci: 
B)center:
, vertices: 
, foci: 
C)center:
, vertices: 
, foci: 
D)center:
, vertices: 
, foci: 
E)center:
, vertices: 
, foci: 
A)center:
, vertices: , foci: B)center:
, vertices: , foci: C)center:
, vertices: , foci: D)center:
, vertices: , foci: E)center:
, vertices: , foci: Question
Find the vertices and foci of the ellipse given by the equation. 
A)vertices:
, foci: 
B)vertices:
, foci: 
C)vertices:
, foci: 
D)vertices:
, foci: 
E)vertices:
, foci: 
A)vertices:
, foci: B)vertices:
, foci: C)vertices:
, foci: D)vertices:
, foci: E)vertices:
, foci: Question
Find the equation in standard form of the hyperbola that satisfies the stated conditions, if it exists. vertices 
and 
, passing through 
A)
B)
C)does not exist
D)
E)
and , passing through A)
B)
C)does not exist
D)
E)
Question
An architect wishes to design a large room 148 feet long that will be a whispering gallery. The ceiling of the room has a cross section that is an ellipse whose foci are to be located 20 feet to the right and the left of center, as shown in the following figure where d is 148 feet and x is 20 feet. 
Find the height h of the elliptical ceiling (to the nearest tenth of a foot).
A)128.0 feet
B)276.0 feet
C)74.3 feet
D)54.0 feet
E)71.2 feet
Find the height h of the elliptical ceiling (to the nearest tenth of a foot).A)128.0 feet
B)276.0 feet
C)74.3 feet
D)54.0 feet
E)71.2 feet
Question
Find the equation in standard form of the hyperbola that satisfies the stated conditions, if it exists. foci 
and 
, asymptotes 
and 
A)
B)
C)
D)does not exist
E)
and , asymptotes and A)
B)
C)
D)does not exist
E)
Question
Use the quadratic formula to solve for y in terms of x . Then use a graphing utility to graph the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the vertices, foci, and asymptotes for the hyperbola given by the equation. 
A)vertices:
, foci: 
, asymptotes: 
B)vertices:
, foci: 
, asymptotes: 
C)vertices:
, foci: 
, asymptotes: 
D)vertices:
, foci: 
, asymptotes: 
E)vertices:
, foci: 
, asymptotes: 
A)vertices:
, foci: , asymptotes: B)vertices:
, foci: , asymptotes: C)vertices:
, foci: , asymptotes: D)vertices:
, foci: , asymptotes: E)vertices:
, foci: , asymptotes: Question
Find the equation in standard form of an ellipse with foci 
that passes through the point 
.
A)
B)
C)
D)
E)
that passes through the point .A)
B)
C)
D)
E)
Question
Graph the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Graph the hyperbola given by the equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the center, vertices, foci, and asymptotes for the hyperbola given by the equation. 
A)center: (0, 6), vertices: (6, 6)(6, - 6), foci:
asymptotes: 
B)center: (0, 6), vertices: (0, 12)(0, 0), foci:
, asymptotes: 
C)center: (0, - 6), vertices: (6, 6)(6, - 6), foci:
asymptotes: 
D)center: (6, 0), vertices: (12, 0)( - 12, 0), foci:
asymptotes: 
E)center: (6, 0), vertices: (6, 6)(6, - 6), foci:
asymptotes: 
A)center: (0, 6), vertices: (6, 6)(6, - 6), foci:
asymptotes: B)center: (0, 6), vertices: (0, 12)(0, 0), foci:
, asymptotes: C)center: (0, - 6), vertices: (6, 6)(6, - 6), foci:
asymptotes: D)center: (6, 0), vertices: (12, 0)( - 12, 0), foci:
asymptotes: E)center: (6, 0), vertices: (6, 6)(6, - 6), foci:
asymptotes: Question
Use the eccentricity to find the equation of the hyperbola in standard form. vertices (1, 6)and (1, 4), eccentricity 2
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Graph the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the quadratic formula to solve for y in terms of x . Then use a graphing utility to graph the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the vertices, foci, and asymptotes for the hyperbola given by the equation. 
A)vertices:
, foci: 
, asymptotes: 
B)vertices:
, foci: 
, asymptotes: 
C)vertices:
, foci: 
, asymptotes: 
D)vertices:
foci: 
, asymptotes: 
E)vertices:
, foci: 
, asymptotes: 
A)vertices:
, foci: , asymptotes: B)vertices:
, foci: , asymptotes: C)vertices:
, foci: , asymptotes: D)vertices:
foci: , asymptotes: E)vertices:
, foci: , asymptotes: Question
A line segment with endpoints on the ellipse that is perpendicular to the major axis and passes through a focus is a latus rectum of the ellipse. Find the length of the latus rectum for the ellipse 
.
A)40
B)2
C)5
D)1
E)10
.A)40
B)2
C)5
D)1
E)10
Question
Find the equation in standard form of the hyperbola with asymptotes 
and 
, and vertices ( 9, 0)and (9, 0).
A)
B)
C)
D)
E)
and , and vertices ( 9, 0)and (9, 0).A)
B)
C)
D)
E)
Question
Find the equation in standard form of the hyperbola with an asymptote slope of 
and foci (2, 1)and (12, 1).
A)
B)
C)
D)
E)
and foci (2, 1)and (12, 1).A)
B)
C)
D)
E)
Question
Question
A circular vent pipe with a diameter of 8.5 inches is placed on a roof that has a slope of 
as shown in the figure below. 
The intersection of the vent pipe and the roof is an ellipse. To the nearest hundredth of an inch, what are the lengths of the major and minor axes?
A)22.89 inches and 4.25 inches
B)9.15 inches and 4.25 inches
C)9.15 inches and 8.50 inches
D)4.25 inches and 3.40 inches
E)8.50 inches and 3.40 inches
as shown in the figure below. The intersection of the vent pipe and the roof is an ellipse. To the nearest hundredth of an inch, what are the lengths of the major and minor axes?A)22.89 inches and 4.25 inches
B)9.15 inches and 4.25 inches
C)9.15 inches and 8.50 inches
D)4.25 inches and 3.40 inches
E)8.50 inches and 3.40 inches
Question
Find the vertices, foci, and asymptotes for the hyperbola given by the equation. 
A)vertices:
, foci: 
, asymptotes: 
B)vertices:
, foci: 
, asymptotes: 
C)vertices:
, foci: 
, asymptotes: 
D)vertices:
, foci: 
, asymptotes: 
E)vertices:
, foci: 
, asymptotes: 
A)vertices:
, foci: , asymptotes: B)vertices:
, foci: , asymptotes: C)vertices:
, foci: , asymptotes: D)vertices:
, foci: , asymptotes: E)vertices:
, foci: , asymptotes: Question
Graph the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A vertical cross section of a cooling tower is a portion of a hyperbola, as shown in the diagram below. The standard form of the equation of the hyperbolic cross section is 
where x and y are measured in feet. The horizontal cross sections of the tower are circles. 
Find the radius of the top of the tower. Round to the nearest foot.
A)90 feet
B)88 feet
C)93 feet
D)87 feet
E)85 feet
where x and y are measured in feet. The horizontal cross sections of the tower are circles. Find the radius of the top of the tower. Round to the nearest foot.A)90 feet
B)88 feet
C)93 feet
D)87 feet
E)85 feet
Question
When a plane exceeds the speed of sound, a sonic boom is produced by the wake of the sound waves. For a plane flying at 13,000 feet, the circular wave front can be given by 
where z is the height of the wave front above Earth. See the diagram below. Note that the xy -plane is Earth s surface, which is approximately flat over small distances. Find and name the equation formed when the wave front hits Earth. 
A)
B)
e
C)
D)
E)
where z is the height of the wave front above Earth. See the diagram below. Note that the xy -plane is Earth s surface, which is approximately flat over small distances. Find and name the equation formed when the wave front hits Earth. A)
B)
eC)
D)
E)
Question
Identify the graph of the equation as a parabola, an ellipse, or a hyperbola. 
A)Ellipse
B)Hyperbola
C)Parabola
A)Ellipse
B)Hyperbola
C)Parabola
Question
Plot the point on a polar coordinate system. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the definition of a hyperbola to find the equation of the hyperbola in standard form. foci (7, 0)and ( - 7, 0); passes through the point 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A vertical cross section of a cooling tower is a portion of a hyperbola, as shown in the diagram below. The standard form of the equation of the hyperbolic cross section is 
where x and y are measured in feet. The horizontal cross sections of the tower are circles. 
What is the smallest radius of a horizontal cross section? Round to the nearest foot.
A)52 feet
B)50 feet
C)72 feet
D)54 feet
E)60 feet
where x and y are measured in feet. The horizontal cross sections of the tower are circles. What is the smallest radius of a horizontal cross section? Round to the nearest foot.A)52 feet
B)50 feet
C)72 feet
D)54 feet
E)60 feet
Question
Use the Conic Identification Theorem to identify the graph of the equation as a parabola, an ellipse, or a hyperbola. 
A)Hyperbola
B)Parabola
C)Ellipse
A)Hyperbola
B)Parabola
C)Ellipse
Question
Use the eccentricity to find the equation of the hyperbola in standard form. center ( - 2, - 6), conjugate axis of length 8 with the transverse axis parallel to the x -axis, eccentricity 3
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the definition of a hyperbola to find the equation of the hyperbola in standard form. foci (9, 0)and ( - 9, 0); passes through the point (9, 24)
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Graph the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the Conic Identification Theorem to identify the graph of the equation as a parabola, an ellipse, or a hyperbola. 
A)Hyperbola
B)Parabola
C)Ellipse
A)Hyperbola
B)Parabola
C)Ellipse
Question
Use the eccentricity to find the equation of the hyperbola in standard form. eccentricity 2, foci (12, 0)and ( - 12, 0)
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the acute angle of rotation a that eliminates the xy term. State approximate solution to the nearest 0.1 . 
A)75.5 °
B)-33.4 °
C)14.5 °
D)22.5 °
E)-22.5 °
A)75.5 °
B)-33.4 °
C)14.5 °
D)22.5 °
E)-22.5 °
Question
Find the equation in standard form of a hyperbola with vertices ( 1, 1)and ( 1, 5)and eccentricity 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Identify the graph of the equation below as a parabola, an ellipse, or a hyperbola. 
A)a parabola
B)an ellipse
C)a hyperbola
A)a parabola
B)an ellipse
C)a hyperbola
Question
Two radio transmitters are positioned along the coast, 600 miles apart as shown below in the diagram (with d equal to 600 miles). A signal is sent simultaneously from each transmitter. The signal from transmitter 
is received by a ship s LORAN 700 microseconds after the ship receives the signal from 
. The radio signals travel at 0.186 mile per microsecond. Find an equation of a hyperbola, with foci at 
and 
, on which the ship is located. Round parameters to the nearest tenth. 
A)
B)
C)
D)
E)
is received by a ship s LORAN 700 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. Find an equation of a hyperbola, with foci at and , on which the ship is located. Round parameters to the nearest tenth. A)
B)
C)
D)
E)
Question
Find the acute angle of rotation a that eliminates the xy term. State approximate solution to the nearest 0.1 . 
A)76.7 °
B)13.3 °
C)9.2 °
D)67.5 °
E)22.5 °
A)76.7 °
B)13.3 °
C)9.2 °
D)67.5 °
E)22.5 °
Question
Sketch the graph of the polar equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Two radio transmitters are positioned along the coast, 250 miles apart. A signal is sent simultaneously from each transmitter. The signal from transmitter 
is received by a ship s LORAN 300 microseconds after the ship receives the signal from 
. The radio signals travel at 0.186 mile per microsecond. 
If the ship is 200 miles east of the y-axis, determine its distance from the coastline (to the nearest mile).
A)865 miles
B)1000 miles
C)459 miles
D)1406 miles
E)1541 miles
is received by a ship s LORAN 300 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. If the ship is 200 miles east of the y-axis, determine its distance from the coastline (to the nearest mile).A)865 miles
B)1000 miles
C)459 miles
D)1406 miles
E)1541 miles
Question
Two radio transmitters are positioned along the coast, 250 miles apart. A signal is sent simultaneously from each transmitter. The signal from transmitter 
is received by a ship s LORAN 800 microseconds after the ship receives the signal from 
. The radio signals travel at 0.186 mile per microsecond. 
Find an equation of a hyperbola, with foci at 
and 
on which the ship is located. Round parameters to the nearest hundredth.
A)
B)
C)
D)
E)
is received by a ship s LORAN 800 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. Find an equation of a hyperbola, with foci at and on which the ship is located. Round parameters to the nearest hundredth.A)
B)
C)
D)
E)
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Deck 8: Topics in Analytic Geometry
1
Find the vertex, focus, and directrix of the parabola given by the equation.
A)vertex: , focus: , directrix:
B)vertex: , focus: , directrix:
C)vertex: , focus: , directrix:
D)vertex: , focus: , directrix:
E)vertex: , focus: , directrix:
A)vertex:
, focus: , directrix: B)vertex:
, focus: , directrix: C)vertex:
, focus: , directrix: D)vertex:
, focus: , directrix: E)vertex:
, focus: , directrix: vertex: , focus: , directrix:
, focus: , directrix: 2
The parabolic mirror in a certain telescope has a diameter of 112 inches and a concave depth of 3.69985 inches. Determine the location of its focus above the vertex. Round to the nearest inch.
A)159 inches
B)212 inches
C)583 inches
D)477 inches
E)265 inches
A)159 inches
B)212 inches
C)583 inches
D)477 inches
E)265 inches
212 inches
3
By using the definition of a parabola, find the equation in standard form of the parabola with V (0, 0), F ( s , 0), and directrix .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
4
The line segment that has endpoints on a parabola, passes through the focus of the parabola, and is perpendicular to the axis of symmetry is called the latus rectum of the parabola. Find the length of the latus rectum for the parabola .
A)152
B)38
C)76
D)57
E)19
Find the length of the latus rectum for the parabola .A)152
B)38
C)76
D)57
E)19
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5
Find the equation in standard form of the parabola that has vertex , has a horizontal axis of symmetry, and passes through the point .
A)
B)
C)
D)
E)
, has a horizontal axis of symmetry, and passes through the point .A)
B)
C)
D)
E)
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6
Find the vertex, focus, and directrix of the parabola given by the equation.
A)vertex: (0, -3), focus: (0, 0), directrix: y = 3
B)vertex: (0, 0), focus: (0, 3), directrix: y = -3
C)vertex: (0, 0), focus: (0, -3), directrix: y = 3
D)vertex: (0, 0), focus: (0, -12), directrix: y = 12
E)vertex: (0, -3), focus: (0, 3), directrix: y = 0
A)vertex: (0, -3), focus: (0, 0), directrix: y = 3
B)vertex: (0, 0), focus: (0, 3), directrix: y = -3
C)vertex: (0, 0), focus: (0, -3), directrix: y = 3
D)vertex: (0, 0), focus: (0, -12), directrix: y = 12
E)vertex: (0, -3), focus: (0, 3), directrix: y = 0
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7
Graph the equation below. =
A)
B)
C)
D)
E)
= A)
B)
C)
D)
E)
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8
Graph the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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9
The surface area of a paraboloid with radius r and depth d is given by . The antenna of a radio telescope is a paraboloid measuring 89 feet across with a depth of 18 feet. Approximate (to the nearest 100 square feet)the surface area of the radio telescope.
A)13,300 ft2
B)7100 ft2
C)1600 ft2
D)25,900 ft2
E)7600 ft2
. The antenna of a radio telescope is a paraboloid measuring 89 feet across with a depth of 18 feet. Approximate (to the nearest 100 square feet)the surface area of the radio telescope.A)13,300 ft2
B)7100 ft2
C)1600 ft2
D)25,900 ft2
E)7600 ft2
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10
Graph the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
Find the equation in standard form of the parabola with vertex at and focus .
A)
B)
C)
D)
E)
and focus .A)
B)
C)
D)
E)
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12
Find the vertex, focus, and directrix of the parabola given by the equation.
A)vertex : , focus : , directrix :
B)vertex : , focus : , directrix :
C)vertex : , focus : , directrix :
D)vertex : , focus : , directrix :
E)vertex : , focus : , directrix :
A)vertex :
, focus : , directrix : B)vertex :
, focus : , directrix : C)vertex :
, focus : , directrix : D)vertex :
, focus : , directrix : E)vertex :
, focus : , directrix : Unlock Deck
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13
Find the vertex of the parabola given by the equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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14
The line segment that has endpoints on a parabola, passes through the focus of the parabola, and is perpendicular to the axis of symmetry is called the latus rectum of the parabola. Find the length of the latus rectum for the parabola .
A)24
B)12
C)36
D)48
E)96
Find the length of the latus rectum for the parabola .A)24
B)12
C)36
D)48
E)96
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15
The Lovell Telescope is a radio telescope located at the Jodrell Bank Observatory in Cheshire, England. The dish of the telescope has the shape of a paraboloid with a diameter of 240 feet. The distance from the vertex of the dish to its focus is 85 feet. The surface area of a paraboloid with radius r and depth d is given by . Approximate (to the nearest 100 square feet)the surface area of the radio telescope.
A)118,900 ft2
B)63,300 ft2
C)50,500 ft2
D)186,500 ft2
E)50,500 ft2.
. Approximate (to the nearest 100 square feet)the surface area of the radio telescope.A)118,900 ft2
B)63,300 ft2
C)50,500 ft2
D)186,500 ft2
E)50,500 ft2.
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16
Ultrasound is used as a nondestructive method of determining whether a support beam for a structure has an internal fracture. In one scanning procedure, if the resulting image is a parabola, engineers know that there is a structural defect. Suppose that a scan produced an image whose equation is . Determine the vertex and focus of the graph of this parabola.
A)vertex: , focus:
B)vertex: , focus:
C)vertex: , focus:
D)vertex: , focus:
E)vertex: , focus:
. Determine the vertex and focus of the graph of this parabola.A)vertex:
, focus: B)vertex:
, focus: C)vertex:
, focus: D)vertex:
, focus: E)vertex:
, focus: Unlock Deck
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17
The antenna of a radio telescope is a paraboloid measuring 66 feet across with a depth of 35 feet. Determine, to the nearest tenth of a foot, the distance from the vertex to the focus of this antenna. Round to the nearest hundredth.
A)2.32 feet
B)9.28 feet
C)15.56 feet
D)31.11 feet
E)7.78 feet
A)2.32 feet
B)9.28 feet
C)15.56 feet
D)31.11 feet
E)7.78 feet
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18
Find the equation in standard form of the parabola with focus and directrix .
A)
B)
C)
D)
E)
and directrix .A)
B)
C)
D)
E)
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19
A fountain in a shopping mall has two parabolic arcs of water intersecting as shown below. The equation of one parabola is and the equation of the second parabola is . How high above the base of the fountain do the parabolas intersect? All dimensions are in feet. Round your answer to the nearest hundredth.
A)5.91 feet
B)6.40 feet
C)2.95 feet
D)3.45 feet
E)8.86 feet
and the equation of the second parabola is . How high above the base of the fountain do the parabolas intersect? All dimensions are in feet. Round your answer to the nearest hundredth.A)5.91 feet
B)6.40 feet
C)2.95 feet
D)3.45 feet
E)8.86 feet
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20
Find the equation in standard form of the parabola with vertex at and focus .
A)
B)
C)
D)
E)
and focus .A)
B)
C)
D)
E)
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21
Find the center, vertices, and foci of the ellipse given by the equation.
A)center: , vertices: , foci:
B)center: , vertices: , foci:
C)center: , vertices: , foci:
D)center: , vertices: , foci:
E)center: , vertices: , foci:
A)center:
, vertices: , foci: B)center:
, vertices: , foci: C)center:
, vertices: , foci: D)center:
, vertices: , foci: E)center:
, vertices: , foci: Unlock Deck
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22
Find the center of the ellipse given by the equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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23
Find the equation in standard form of the ellipse, given the information provided. vertices , foci at
A)
B)
C)
D)
E)
, foci at A)
B)
C)
D)
E)
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24
Use the eccentricity of the ellipse to find its equation in standard form. eccentricity , major axis of length 28 on the y -axis, center at (0, 0)
A)
B)
C)
D)
E)
, major axis of length 28 on the y -axis, center at (0, 0)A)
B)
C)
D)
E)
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25
A circular vent pipe with a diameter of 6.5 inches is placed on a roof that has a slope of as shown in the figure below. Use the slope to find the value of h . Round to the nearest hundredths.
A)2.44 inches
B)17.33 inches
C)4.88 inches
D)4.33 inches
E)9.75 inches
as shown in the figure below. Use the slope to find the value of h . Round to the nearest hundredths.A)2.44 inches
B)17.33 inches
C)4.88 inches
D)4.33 inches
E)9.75 inches
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26
Find the center, vertices, and foci of the ellipse given by the equation.
A)center: , vertices: , foci:
B)center: , vertices: , foci:
C)center: , vertices: , foci:
D)center: , vertices: , foci:
E)center: , vertices: , foci:
A)center:
, vertices: , foci: B)center:
, vertices: , foci: C)center:
, vertices: , foci: D)center:
, vertices: , foci: E)center:
, vertices: , foci: Unlock Deck
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27
Find the vertices and foci of the ellipse given by the equation.
A)vertices:
B)vertices:
C)vertices:
D)vertices:
E)vertices:
A)vertices:
B)vertices:
C)vertices:
D)vertices:
E)vertices:
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28
Use the eccentricity of the ellipse to find its equation in standard form. eccentricity , foci at
A)
B)
C)
D)
E)
, foci at A)
B)
C)
D)
E)
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29
Find the equation in standard form of the ellipse, given the information provided. major axis of length 20, center at ; ellipse passes through
A)
B)
C)
D)
E)
; ellipse passes through A)
B)
C)
D)
E)
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30
Graph the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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31
Find the equation in standard form of the ellipse with center (8, 5), minor axis parallel to the x -axis and of length 6, and that passes through point (9.5, 11).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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32
Graph the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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33
Find the equation in standard form of an ellipse with eccentricity , center at (0, 0), and major axis on the x -axis and of length 14.
A)
B)
C)
D)
E)
, center at (0, 0), and major axis on the x -axis and of length 14.A)
B)
C)
D)
E)
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34
Find the equation in standard form of an ellipse with center at (0, 0)minor axis of length 24, and foci at (0, -16)and (0, 16).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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35
Find the equation in standard form of the ellipse, given the information provided. center , vertices , foci at
A)
B)
C)
D)
E)
, vertices , foci at A)
B)
C)
D)
E)
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36
Find the vertices and foci of the ellipse given by the equation.
A)vertices: , foci:
B)vertices: , foci:
C)vertices: , foci:
D)vertices: , foci:
E)vertices: , foci:
A)vertices:
, foci: B)vertices:
, foci: C)vertices:
, foci: D)vertices:
, foci: E)vertices:
, foci: Unlock Deck
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37
Use the eccentricity of the ellipse to find its equation in standard form. eccentricity , major axis of length 18 on the x -axis, center at
A)
B)
C)
D)
E)
, major axis of length 18 on the x -axis, center at A)
B)
C)
D)
E)
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38
Use the eccentricity of the ellipse to find its equation in standard form. foci at , eccentricity
A)
B)
C)
D)
E)
, eccentricity A)
B)
C)
D)
E)
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39
Find the center, vertices, and foci of the ellipse given by the equation.
A)center: , vertices: , foci:
B)center: , vertices: , foci:
C)center: , vertices: , foci:
D)center: , vertices: , foci:
E)center: , vertices: , foci:
A)center:
, vertices: , foci: B)center:
, vertices: , foci: C)center:
, vertices: , foci: D)center:
, vertices: , foci: E)center:
, vertices: , foci: Unlock Deck
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40
Find the vertices and foci of the ellipse given by the equation.
A)vertices: , foci:
B)vertices: , foci:
C)vertices: , foci:
D)vertices: , foci:
E)vertices: , foci:
A)vertices:
, foci: B)vertices:
, foci: C)vertices:
, foci: D)vertices:
, foci: E)vertices:
, foci: Unlock Deck
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41
Find the equation in standard form of the hyperbola that satisfies the stated conditions, if it exists. vertices and , passing through
A)
B)
C)does not exist
D)
E)
and , passing through A)
B)
C)does not exist
D)
E)
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42
An architect wishes to design a large room 148 feet long that will be a whispering gallery. The ceiling of the room has a cross section that is an ellipse whose foci are to be located 20 feet to the right and the left of center, as shown in the following figure where d is 148 feet and x is 20 feet. Find the height h of the elliptical ceiling (to the nearest tenth of a foot).
A)128.0 feet
B)276.0 feet
C)74.3 feet
D)54.0 feet
E)71.2 feet
Find the height h of the elliptical ceiling (to the nearest tenth of a foot).A)128.0 feet
B)276.0 feet
C)74.3 feet
D)54.0 feet
E)71.2 feet
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43
Find the equation in standard form of the hyperbola that satisfies the stated conditions, if it exists. foci and , asymptotes and
A)
B)
C)
D)does not exist
E)
and , asymptotes and A)
B)
C)
D)does not exist
E)
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44
Use the quadratic formula to solve for y in terms of x . Then use a graphing utility to graph the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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45
Find the vertices, foci, and asymptotes for the hyperbola given by the equation.
A)vertices: , foci: , asymptotes:
B)vertices: , foci: , asymptotes:
C)vertices: , foci: , asymptotes:
D)vertices: , foci: , asymptotes:
E)vertices: , foci: , asymptotes:
A)vertices:
, foci: , asymptotes: B)vertices:
, foci: , asymptotes: C)vertices:
, foci: , asymptotes: D)vertices:
, foci: , asymptotes: E)vertices:
, foci: , asymptotes: Unlock Deck
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46
Find the equation in standard form of an ellipse with foci that passes through the point .
A)
B)
C)
D)
E)
that passes through the point .A)
B)
C)
D)
E)
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47
Graph the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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48
Graph the hyperbola given by the equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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49
Find the center, vertices, foci, and asymptotes for the hyperbola given by the equation.
A)center: (0, 6), vertices: (6, 6)(6, - 6), foci: asymptotes:
B)center: (0, 6), vertices: (0, 12)(0, 0), foci: , asymptotes:
C)center: (0, - 6), vertices: (6, 6)(6, - 6), foci: asymptotes:
D)center: (6, 0), vertices: (12, 0)( - 12, 0), foci: asymptotes:
E)center: (6, 0), vertices: (6, 6)(6, - 6), foci: asymptotes:
A)center: (0, 6), vertices: (6, 6)(6, - 6), foci:
asymptotes: B)center: (0, 6), vertices: (0, 12)(0, 0), foci:
, asymptotes: C)center: (0, - 6), vertices: (6, 6)(6, - 6), foci:
asymptotes: D)center: (6, 0), vertices: (12, 0)( - 12, 0), foci:
asymptotes: E)center: (6, 0), vertices: (6, 6)(6, - 6), foci:
asymptotes: Unlock Deck
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50
Use the eccentricity to find the equation of the hyperbola in standard form. vertices (1, 6)and (1, 4), eccentricity 2
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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51
Graph the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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52
Use the quadratic formula to solve for y in terms of x . Then use a graphing utility to graph the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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53
Find the vertices, foci, and asymptotes for the hyperbola given by the equation.
A)vertices: , foci: , asymptotes:
B)vertices: , foci: , asymptotes:
C)vertices: , foci: , asymptotes:
D)vertices: foci: , asymptotes:
E)vertices: , foci: , asymptotes:
A)vertices:
, foci: , asymptotes: B)vertices:
, foci: , asymptotes: C)vertices:
, foci: , asymptotes: D)vertices:
foci: , asymptotes: E)vertices:
, foci: , asymptotes: Unlock Deck
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54
A line segment with endpoints on the ellipse that is perpendicular to the major axis and passes through a focus is a latus rectum of the ellipse. Find the length of the latus rectum for the ellipse .
A)40
B)2
C)5
D)1
E)10
.A)40
B)2
C)5
D)1
E)10
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55
Find the equation in standard form of the hyperbola with asymptotes and , and vertices ( 9, 0)and (9, 0).
A)
B)
C)
D)
E)
and , and vertices ( 9, 0)and (9, 0).A)
B)
C)
D)
E)
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56
Find the equation in standard form of the hyperbola with an asymptote slope of and foci (2, 1)and (12, 1).
A)
B)
C)
D)
E)
and foci (2, 1)and (12, 1).A)
B)
C)
D)
E)
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57
An architect wishes to design a large room that will be a whispering gallery. The ceiling of the room has a cross section that is an ellipse with a major axis measuring 286 feet and a minor axis measuring 90 feet. Assume the center is at (0, 0)and the major axis lies on the x -axis. How far to the right and left of center are the foci located? Approximate the answer to the nearest tenth of a foot.
A)135.7 ft
B)271.5 ft
C)45.0 ft
D)143.0 ft
E)196.0 ft
A)135.7 ft
B)271.5 ft
C)45.0 ft
D)143.0 ft
E)196.0 ft
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58
A circular vent pipe with a diameter of 8.5 inches is placed on a roof that has a slope of as shown in the figure below. The intersection of the vent pipe and the roof is an ellipse. To the nearest hundredth of an inch, what are the lengths of the major and minor axes?
A)22.89 inches and 4.25 inches
B)9.15 inches and 4.25 inches
C)9.15 inches and 8.50 inches
D)4.25 inches and 3.40 inches
E)8.50 inches and 3.40 inches
as shown in the figure below. The intersection of the vent pipe and the roof is an ellipse. To the nearest hundredth of an inch, what are the lengths of the major and minor axes?A)22.89 inches and 4.25 inches
B)9.15 inches and 4.25 inches
C)9.15 inches and 8.50 inches
D)4.25 inches and 3.40 inches
E)8.50 inches and 3.40 inches
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59
Find the vertices, foci, and asymptotes for the hyperbola given by the equation.
A)vertices: , foci: , asymptotes:
B)vertices: , foci: , asymptotes:
C)vertices: , foci: , asymptotes:
D)vertices: , foci: , asymptotes:
E)vertices: , foci: , asymptotes:
A)vertices:
, foci: , asymptotes: B)vertices:
, foci: , asymptotes: C)vertices:
, foci: , asymptotes: D)vertices:
, foci: , asymptotes: E)vertices:
, foci: , asymptotes: Unlock Deck
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60
Graph the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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61
A vertical cross section of a cooling tower is a portion of a hyperbola, as shown in the diagram below. The standard form of the equation of the hyperbolic cross section is where x and y are measured in feet. The horizontal cross sections of the tower are circles. Find the radius of the top of the tower. Round to the nearest foot.
A)90 feet
B)88 feet
C)93 feet
D)87 feet
E)85 feet
where x and y are measured in feet. The horizontal cross sections of the tower are circles. Find the radius of the top of the tower. Round to the nearest foot.A)90 feet
B)88 feet
C)93 feet
D)87 feet
E)85 feet
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62
When a plane exceeds the speed of sound, a sonic boom is produced by the wake of the sound waves. For a plane flying at 13,000 feet, the circular wave front can be given by where z is the height of the wave front above Earth. See the diagram below. Note that the xy -plane is Earth s surface, which is approximately flat over small distances. Find and name the equation formed when the wave front hits Earth.
A)
B) e
C)
D)
E)
where z is the height of the wave front above Earth. See the diagram below. Note that the xy -plane is Earth s surface, which is approximately flat over small distances. Find and name the equation formed when the wave front hits Earth. A)
B)
eC)
D)
E)
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63
Identify the graph of the equation as a parabola, an ellipse, or a hyperbola.
A)Ellipse
B)Hyperbola
C)Parabola
A)Ellipse
B)Hyperbola
C)Parabola
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64
Plot the point on a polar coordinate system.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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65
Use the definition of a hyperbola to find the equation of the hyperbola in standard form. foci (7, 0)and ( - 7, 0); passes through the point
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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66
A vertical cross section of a cooling tower is a portion of a hyperbola, as shown in the diagram below. The standard form of the equation of the hyperbolic cross section is where x and y are measured in feet. The horizontal cross sections of the tower are circles. What is the smallest radius of a horizontal cross section? Round to the nearest foot.
A)52 feet
B)50 feet
C)72 feet
D)54 feet
E)60 feet
where x and y are measured in feet. The horizontal cross sections of the tower are circles. What is the smallest radius of a horizontal cross section? Round to the nearest foot.A)52 feet
B)50 feet
C)72 feet
D)54 feet
E)60 feet
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67
Use the Conic Identification Theorem to identify the graph of the equation as a parabola, an ellipse, or a hyperbola.
A)Hyperbola
B)Parabola
C)Ellipse
A)Hyperbola
B)Parabola
C)Ellipse
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68
Use the eccentricity to find the equation of the hyperbola in standard form. center ( - 2, - 6), conjugate axis of length 8 with the transverse axis parallel to the x -axis, eccentricity 3
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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69
Use the definition of a hyperbola to find the equation of the hyperbola in standard form. foci (9, 0)and ( - 9, 0); passes through the point (9, 24)
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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70
Graph the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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71
Use the Conic Identification Theorem to identify the graph of the equation as a parabola, an ellipse, or a hyperbola.
A)Hyperbola
B)Parabola
C)Ellipse
A)Hyperbola
B)Parabola
C)Ellipse
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72
Use the eccentricity to find the equation of the hyperbola in standard form. eccentricity 2, foci (12, 0)and ( - 12, 0)
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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73
Find the acute angle of rotation a that eliminates the xy term. State approximate solution to the nearest 0.1 .
A)75.5 °
B)-33.4 °
C)14.5 °
D)22.5 °
E)-22.5 °
A)75.5 °
B)-33.4 °
C)14.5 °
D)22.5 °
E)-22.5 °
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74
Find the equation in standard form of a hyperbola with vertices ( 1, 1)and ( 1, 5)and eccentricity .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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75
Identify the graph of the equation below as a parabola, an ellipse, or a hyperbola.
A)a parabola
B)an ellipse
C)a hyperbola
A)a parabola
B)an ellipse
C)a hyperbola
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76
Two radio transmitters are positioned along the coast, 600 miles apart as shown below in the diagram (with d equal to 600 miles). A signal is sent simultaneously from each transmitter. The signal from transmitter is received by a ship s LORAN 700 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. Find an equation of a hyperbola, with foci at and , on which the ship is located. Round parameters to the nearest tenth.
A)
B)
C)
D)
E)
is received by a ship s LORAN 700 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. Find an equation of a hyperbola, with foci at and , on which the ship is located. Round parameters to the nearest tenth. A)
B)
C)
D)
E)
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77
Find the acute angle of rotation a that eliminates the xy term. State approximate solution to the nearest 0.1 .
A)76.7 °
B)13.3 °
C)9.2 °
D)67.5 °
E)22.5 °
A)76.7 °
B)13.3 °
C)9.2 °
D)67.5 °
E)22.5 °
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78
Sketch the graph of the polar equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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79
Two radio transmitters are positioned along the coast, 250 miles apart. A signal is sent simultaneously from each transmitter. The signal from transmitter is received by a ship s LORAN 300 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. If the ship is 200 miles east of the y-axis, determine its distance from the coastline (to the nearest mile).
A)865 miles
B)1000 miles
C)459 miles
D)1406 miles
E)1541 miles
is received by a ship s LORAN 300 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. If the ship is 200 miles east of the y-axis, determine its distance from the coastline (to the nearest mile).A)865 miles
B)1000 miles
C)459 miles
D)1406 miles
E)1541 miles
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80
Two radio transmitters are positioned along the coast, 250 miles apart. A signal is sent simultaneously from each transmitter. The signal from transmitter is received by a ship s LORAN 800 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. Find an equation of a hyperbola, with foci at and on which the ship is located. Round parameters to the nearest hundredth.
A)
B)
C)
D)
E)
is received by a ship s LORAN 800 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. Find an equation of a hyperbola, with foci at and on which the ship is located. Round parameters to the nearest hundredth.A)
B)
C)
D)
E)
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