Question 1

Sketch the graph of the polar equation.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

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.

Accepted Answer

A) 5.91 feet 
B) 6.40 feet 
C) 2.95 feet 
D) 3.45 feet 
E) 8.86 feet 
A) 5.91 feet 
B) 6.40 feet 
C) 2.95 feet 
D) 3.45 feet 
E) 8.86 feet

Question 3

Graph the equation below.   =

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

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.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

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.

Accepted Answer

A) 2.44 inches 
B) 17.33 inches 
C) 4.88 inches 
D) 4.33 inches 
E) 9.75 inches 
A) 2.44 inches 
B) 17.33 inches 
C) 4.88 inches 
D) 4.33 inches 
E) 9.75 inches

Question 6

Find the equation in standard form of the hyperbola that satisfies the stated conditions, if it exists. vertices   and   , passing through

Accepted Answer

A)    
B)    
C) does not exist 
D)    
E)    
A)    
B)    
C) does not exist 
D)    
E)

Question 7

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.

Accepted Answer

A) vertex:   , focus:   
B) vertex:   , focus:   
C) vertex:   , focus:   
D) vertex:   , focus:   
E) vertex:   , focus:   
A) vertex:   , focus:   
B) vertex:   , focus:   
C) vertex:   , focus:   
D) vertex:   , focus:   
E) vertex:   , focus:

Question 8

Graph the hyperbola given by the equation   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Sketch the graph of the polar equation.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Find the vertex of the parabola given by the equation   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Find a rectangular form of the equation   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Find the vertex, focus, and directrix of the parabola given by the equation.

Accepted Answer

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 13

Find a polar form of the equation   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Find the equation in standard form of the parabola with focus   and directrix   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Find the equation in standard form of the ellipse, given the information provided. center   , vertices   , foci at

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Find the equation in standard form of the parabola that has vertex   , has a horizontal axis of symmetry, and passes through the point   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

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)

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Find a rectangular form of the equation   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Find the equation in standard form of the hyperbola that satisfies the stated conditions, if it exists. foci   and   , asymptotes   and

Accepted Answer

A)    
B)    
C)    
D) does not exist 
E)    
A)    
B)    
C)    
D) does not exist 
E)

Question 20

Use the Conic Identification Theorem to identify the graph of the equation as a parabola, an ellipse, or a hyperbola.

Accepted Answer

A) Hyperbola 
B) Parabola 
C) Ellipse 
A) Hyperbola 
B) Parabola 
C) Ellipse

Sketch the graph of the polar equation.

Graph the equation below. =

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.

Find the equation in standard form of the hyperbola that satisfies the stated conditions, if it exists. vertices and , passing through

Graph the hyperbola given by the equation .

Sketch the graph of the polar equation.

Find the vertex of the parabola given by the equation .

Find a rectangular form of the equation .

Find the vertex, focus, and directrix of the parabola given by the equation.

Find a polar form of the equation .

Find the equation in standard form of the parabola with focus and directrix .

Find the equation in standard form of the ellipse, given the information provided. center , vertices , foci at

Find the equation in standard form of the parabola that has vertex , has a horizontal axis of symmetry, and passes through the point .

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)

Find a rectangular form of the equation .

Find the equation in standard form of the hyperbola that satisfies the stated conditions, if it exists. foci and , asymptotes and

Use the Conic Identification Theorem to identify the graph of the equation as a parabola, an ellipse, or a hyperbola.

Equations and Inequalities

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Polynomial and Rational Functions

Exponential and Logarithmic Functions

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Exam 8: Topics in Analytic Geometry

Sketch the graph of the polar equation.

Graph the equation below. =

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.

Find the equation in standard form of the hyperbola that satisfies the stated conditions, if it exists. vertices and , passing through

Graph the hyperbola given by the equation .

Sketch the graph of the polar equation.

Find the vertex of the parabola given by the equation .

Find a rectangular form of the equation .

Find the vertex, focus, and directrix of the parabola given by the equation.

Find a polar form of the equation .

Find the equation in standard form of the parabola with focus and directrix .

Find the equation in standard form of the ellipse, given the information provided. center , vertices , foci at

Find the equation in standard form of the parabola that has vertex , has a horizontal axis of symmetry, and passes through the point .

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)

Find a rectangular form of the equation .

Find the equation in standard form of the hyperbola that satisfies the stated conditions, if it exists. foci and , asymptotes and

Use the Conic Identification Theorem to identify the graph of the equation as a parabola, an ellipse, or a hyperbola.

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Systems of Equations and Inequalities

Matrices

Sequences, Series, and Probability

Preliminary Concepts

Filters