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Deck 10: Conics, Parametric Equations, and Polar Coordinates
Full screen (f)
Question
Find the corresponding rectangular coordinates for the point 
. Round your answer to three decimal places.
A)
B)
C)
D)
E)
. Round your answer to three decimal places.A)
B)
C)
D)
E)
Question
Match the graph with its polar equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the second derivative 
of the parametric equations 
. Round your answer to two decimal places, if necessary.
A) 0
B) 0.88
C)
D) 1.14
E)
of the parametric equations . Round your answer to two decimal places, if necessary.A) 0
B) 0.88
C)
D) 1.14
E)
Question
Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results. 
A) eccentricity:
Distance from pole to directrix:
The graph is an ellipse.
B) eccentricity:
Distance from pole to directrix:
The graph is a hyperbola.
C) eccentricity:
Distance from pole to directrix:
The graph is a hyperbola.
D) eccentricity:
Distance from pole to directrix:
The graph is an ellipse.
E) eccentricity:
Distance from pole to directrix:
The graph is an ellipse.
A) eccentricity:
Distance from pole to directrix:
The graph is an ellipse.
B) eccentricity:
Distance from pole to directrix:
The graph is a hyperbola.
C) eccentricity:
Distance from pole to directrix:
The graph is a hyperbola.
D) eccentricity:
Distance from pole to directrix:
The graph is an ellipse.
E) eccentricity:
Distance from pole to directrix:
The graph is an ellipse.
Question
Find all points (if any) of horizontal and vertical tangency to the curve 
.
A) horizontal tangents:
, vertical tangent: none
B) horizontal tangent: none, vertical tangents:
C) horizontal tangents:
, vertical tangent: none
D) horizontal tangent: none, vertical tangents:
E) horizontal tangent: none, vertical tangent: none
.A) horizontal tangents:
, vertical tangent: noneB) horizontal tangent: none, vertical tangents:
C) horizontal tangents:
, vertical tangent: noneD) horizontal tangent: none, vertical tangents:
E) horizontal tangent: none, vertical tangent: none
Question
Find the eccentricity of the ellipse given by 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Match the equation with its graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
For the given point in rectangular coordinates, find two sets of polar coordinates for the point for 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Identify the graph for the polar equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the area of the surface generated by revolving the curve about the given axis. 
(i) x-axis; (ii) y-axis
A)
B)
C)
D)
E)
(i) x-axis; (ii) y-axisA)
B)
C)
D)
E)
Question
Match the graph with its polar equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find two sets of polar coordinates for the point 
for 
.
A)
B)
C)
D)
E)
for .A)
B)
C)
D)
E)
Question
Match the equation with its graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results. 
A) eccentricity:
distance from pole to directrix: 
The graph is an ellipse. 
B) eccentricity:
distance from pole to directrix: 
The graph is an ellipse. 
C) eccentricity:
distance from pole to directrix: 
The graph is an ellipse. 
D) eccentricity:
distance from pole to directrix: 
The graph is a hyperbola. 
E) eccentricity:
distance from pole to directrix: 
The graph is a hyperbola. 
A) eccentricity:
distance from pole to directrix: The graph is an ellipse. B) eccentricity:
distance from pole to directrix: The graph is an ellipse. C) eccentricity:
distance from pole to directrix: The graph is an ellipse. D) eccentricity:
distance from pole to directrix: The graph is a hyperbola. E) eccentricity:
distance from pole to directrix: The graph is a hyperbola. Question
Identify the graph for the polar equation 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Match the equation with its graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Identify the graph for the polar equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Match the graph with its polar equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Match the equation with its graph. 
A)
B)
C)
D)
E) none of these
A)
B)
C)
D)
E) none of these
Question
Find two sets of polar coordinates for the point 
for 
.
A)
B)
C)
D)
E)
for .A)
B)
C)
D)
E)
Question
Find a polar equation for the parabola with its focus at the pole and vertex 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find 
and 
if possible, and find the slope and concavity (if possible) at the point corresponding to t = 2. 
A)
: slope 
and concave up
B)
slope 8 and concave down
C)
slope 16 and concave up
D)
: slope -8 and concave down
E)
: slope 
and concave up
and if possible, and find the slope and concavity (if possible) at the point corresponding to t = 2. A)
: slope and concave upB)
slope 8 and concave downC)
slope 16 and concave upD)
: slope -8 and concave downE)
: slope and concave up Question
Find the center, foci, and vertices of the hyperbola. 
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 eccentricity of the polar equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find a polar equation for the hyperbola with its focus at the pole, eccentricity 
, and directrix 
.
A)
B)
C)
D)
E)
, and directrix .A)
B)
C)
D)
E)
Question
Find the vertex of the parabola given by 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the distance from the pole to the directrix for the conic 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find the center of the ellipse given by 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the area of the surface generated by revolving the curve 
about the x-axis on the interval 
.
A)
B)
C)
D)
E)
about the x-axis on the interval .A)
B)
C)
D)
E)
Question
Identify the conic for the polar equation 
when 
.
A) ellipse
B) parabola
C) hyperbola
when .A) ellipse
B) parabola
C) hyperbola
Question
Find 
and 
if possible, and find the slope and concavity (if possible) at the point corresponding to 
. 
A)
at 
: slope 1 and concave up
B)
at 
: slope -1 and concave up
C)
at 
: slope -1 and concave down
D)
at 
: slope 1 and concave down
E)
at 
: slope of -1 and concave up
and if possible, and find the slope and concavity (if possible) at the point corresponding to . A)
at : slope 1 and concave upB)
at : slope -1 and concave upC)
at : slope -1 and concave downD)
at : slope 1 and concave downE)
at : slope of -1 and concave up Question
Find the second derivative 
of the parametric equations 
.
A)
B)
C)
D)
E)
of the parametric equations . A)
B)
C)
D)
E)
Question
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 
A) parabola
B) ellipse
C) circle
D) hyperbola
A) parabola
B) ellipse
C) circle
D) hyperbola
Question
Find an equation of the hyperbola with vertices 
and asymptotes 
.
A)
B)
C)
D)
E)
and asymptotes .A)
B)
C)
D)
E)
Question
Find an equation of the parabola with vertex 
and directrix 
.
A)
B)
C)
D)
E)
and directrix .A)
B)
C)
D)
E)
Question
Find the length of the curve 
over the interval 
. Round your answer to two decimal places.
A) 0.58
B) 19.05
C) 11.00
D) 6.35
E) 1.73
over the interval . Round your answer to two decimal places. A) 0.58
B) 19.05
C) 11.00
D) 6.35
E) 1.73
Question
Convert the polar equation to rectangular form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find a polar equation for the ellipse with its focus at the pole and vertices 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find a polar equation for the ellipse with its focus at the pole, eccentricity 
, and directrix 
.
A)
B)
C)
D)
E)
, and directrix .A)
B)
C)
D)
E)
Question
Find all points (if any) of horizontal and vertical tangency to the curve 
.
A) horizontal tangents:
, vertical tangents: 
B) horizontal tangents:
, vertical tangents: 
C) horizontal tangent:
, vertical tangent: 
D) horizontal tangents:
, vertical tangents: 
E) horizontal tangent:
, vertical tangent: 
.A) horizontal tangents:
, vertical tangents: B) horizontal tangents:
, vertical tangents: C) horizontal tangent:
, vertical tangent: D) horizontal tangents:
, vertical tangents: E) horizontal tangent:
, vertical tangent: Question
Find the area of the surface generated by revolving the curve 
about the y-axis on the interval 
. Round your answer to two decimal places.
A) 1436.54
B) 1413.69
C) 1401.46
D) 706.85
E) 2132.77
about the y-axis on the interval . Round your answer to two decimal places. A) 1436.54
B) 1413.69
C) 1401.46
D) 706.85
E) 2132.77
Question
Find the arc length of the curve on the given interval. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the arc length of the curve on the given interval. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine the t intervals on which the curve 
is concave downward or concave upward.
A) concave downward:
; concave upward: 
B) concave downward:
; concave upward: 
C) concave downward:
D) concave upward:
E) concave downward:
is concave downward or concave upward.A) concave downward:
; concave upward: B) concave downward:
; concave upward: C) concave downward:
D) concave upward:
E) concave downward:
Question
Use the result, "the set of parametric equations for the line passing through 
and 
is 
" to find a set of parametric equations for the line passing through 
and 
.
A)
B)
C)
D)
E)
and is " to find a set of parametric equations for the line passing through and .A)
B)
C)
D)
E)
Question
The path of a projectile is modeled by the parametric equations 
and 
where x and y are measured in feet. Use a graphing utility to approximate the range of the projectile. Round your answer to two decimal places.
A) 335.33 ft
B) 558.88 ft
C) 73.76 ft
D) 419.16 ft
E) 209.58 ft
and where x and y are measured in feet. Use a graphing utility to approximate the range of the projectile. Round your answer to two decimal places.A) 335.33 ft
B) 558.88 ft
C) 73.76 ft
D) 419.16 ft
E) 209.58 ft
Question
Find the center, foci, vertices, and eccentricity of the ellipse. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find a set of parametric equations for the rectangular equation 
that satisfies the condition 
at the point 
.
A)
B)
C)
D)
E)
that satisfies the condition at the point .A)
B)
C)
D)
E)
Question
Convert the polar equation to rectangular form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Identify any points at which the cycloid 
is not smooth.
A) not smooth when
B) smooth everywhere
C) not smooth when
D) not smooth when
E) not smooth when
is not smooth.A) not smooth when
B) smooth everywhere
C) not smooth when
D) not smooth when
E) not smooth when
Question
Find all points of intersection of the graphs of the equations. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the corresponding rectangular equation for the curve represented by the parametric equations 
by eliminating the parameter.
A)
B)
C)
D)
E)
by eliminating the parameter.A)
B)
C)
D)
E)
Question
Write the corresponding rectangular equation for the curve represented by the parametric equations 
by eliminating the parameter.
A)
B)
C)
D)
E)
by eliminating the parameter.A)
B)
C)
D)
E)
Question
Find the area of inside 
and outside 
by sketching the graph of the equations using the graphing utility.
A)
B)
C)
D)
E)
and outside by sketching the graph of the equations using the graphing utility. A)
B)
C)
D)
E)
Question
Find the length of the curve over the given interval. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine the t intervals on which the curve 
is concave downward or concave upward.
A) concave downward:
; concave upward: 
B) concave downward:
; concave upward: 
C) concave downward:
; concave upward: 
D) concave downward:
; concave upward: 
E) concave downward:
; concave upward: 
is concave downward or concave upward.A) concave downward:
; concave upward: B) concave downward:
; concave upward: C) concave downward:
; concave upward: D) concave downward:
; concave upward: E) concave downward:
; concave upward: Question
Write the corresponding rectangular equation for the curve represented by the parametric equation 
by eliminating the parameter.
A)
B)
C)
D)
E)
by eliminating the parameter.A)
B)
C)
D)
E)
Question
Find a set of parametric equations for the rectangular equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the area of the surface formed by revolving about the 
axis the following curve over the given interval. 
A)
B)
C)
D)
E)
axis the following curve over the given interval. A)
B)
C)
D)
E)
Question
Sketch the curve represented by the parametric equations 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the arc length of the curve 
on the interval 
. Round your answer to three decimal places.
A) 287.453
B) 191.635
C) 193.606
D) 66.480
E) 99.721
on the interval . Round your answer to three decimal places.A) 287.453
B) 191.635
C) 193.606
D) 66.480
E) 99.721
Question
Find a set of parametric equations for the rectangular equation 
that satisfies the condition 
at the point 
.
A)
B)
C)
D)
E)
that satisfies the condition at the point .A)
B)
C)
D)
E)
Question
Find the area of the region lying between the loops of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the area of the inner loop of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the area of the surface generated by revolving the curve about the given axis. 
(i) x-axis; (ii) y-axis
A)
B)
C)
D)
E)
(i) x-axis; (ii) y-axisA)
B)
C)
D)
E)
Question
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 
A) parabola
B) circle
C) ellipse
D) hyperbola
A) parabola
B) circle
C) ellipse
D) hyperbola
Question
Find the foci of the ellipse given by 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Use the result, "the set of parametric equations for the ellipse is 
" to find a set of parametric equations for the ellipse with vertices 
and 
and with foci at 
and 
.
A)
B)
C)
D)
E)
" to find a set of parametric equations for the ellipse with vertices and and with foci at and . A)
B)
C)
D)
E)
Question
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 
A) circle
B) hyperbola
C) ellipse
D) parabola
A) circle
B) hyperbola
C) ellipse
D) parabola
Question
Identify any points at which the Folium of Descartes 
is not smooth. Round your answer to two decimal places, if necessary.
A) not smooth when
B) not smooth when
C) not smooth when
D) smooth everywhere
E) not smooth when
is not smooth. Round your answer to two decimal places, if necessary.A) not smooth when
B) not smooth when
C) not smooth when
D) smooth everywhere
E) not smooth when
Question
Find the distance from the pole to the directrix for the conic 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Question
Find the distance from the pole to the directrix for the conic 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the eccentricity of the polar equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the vertex, focus, and directrix of the parabola and sketch its graph. 
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 area of one petal of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle 
with the horizontal and having an initial velocity of 
feet per second is given by 
and 
. The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of 
degrees with the horizontal at a speed of 95 miles per hour as shown in the figure. Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run using the parametric equations 
and 
. Round your answer to one decimal place. 
A)
B)
C)
D)
E)
with the horizontal and having an initial velocity of feet per second is given by and . The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of degrees with the horizontal at a speed of 95 miles per hour as shown in the figure. Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run using the parametric equations and . Round your answer to one decimal place. A)
B)
C)
D)
E)
Question
Find the area of the interior of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
For the given point in polar coordinates, find the corresponding rectangular coordinates for the point. 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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Deck 10: Conics, Parametric Equations, and Polar Coordinates
1
Find the corresponding rectangular coordinates for the point . Round your answer to three decimal places.
A)
B)
C)
D)
E)
. Round your answer to three decimal places.A)
B)
C)
D)
E)
E
2
Match the graph with its polar equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
A
3
Find the second derivative of the parametric equations . Round your answer to two decimal places, if necessary.
A) 0
B) 0.88
C)
D) 1.14
E)
of the parametric equations . Round your answer to two decimal places, if necessary.A) 0
B) 0.88
C)
D) 1.14
E)
A
4
Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results.
A) eccentricity:
Distance from pole to directrix:
The graph is an ellipse.
B) eccentricity:
Distance from pole to directrix:
The graph is a hyperbola.
C) eccentricity:
Distance from pole to directrix:
The graph is a hyperbola.
D) eccentricity:
Distance from pole to directrix:
The graph is an ellipse.
E) eccentricity:
Distance from pole to directrix:
The graph is an ellipse.
A) eccentricity:
Distance from pole to directrix:
The graph is an ellipse.
B) eccentricity:
Distance from pole to directrix:
The graph is a hyperbola.
C) eccentricity:
Distance from pole to directrix:
The graph is a hyperbola.
D) eccentricity:
Distance from pole to directrix:
The graph is an ellipse.
E) eccentricity:
Distance from pole to directrix:
The graph is an ellipse.
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5
Find all points (if any) of horizontal and vertical tangency to the curve .
A) horizontal tangents: , vertical tangent: none
B) horizontal tangent: none, vertical tangents:
C) horizontal tangents: , vertical tangent: none
D) horizontal tangent: none, vertical tangents:
E) horizontal tangent: none, vertical tangent: none
.A) horizontal tangents:
, vertical tangent: noneB) horizontal tangent: none, vertical tangents:
C) horizontal tangents:
, vertical tangent: noneD) horizontal tangent: none, vertical tangents:
E) horizontal tangent: none, vertical tangent: none
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6
Find the eccentricity of the ellipse given by .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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7
Match the equation with its graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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8
For the given point in rectangular coordinates, find two sets of polar coordinates for the point for .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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9
Identify the graph for the polar equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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10
Find the area of the surface generated by revolving the curve about the given axis. (i) x-axis; (ii) y-axis
A)
B)
C)
D)
E)
(i) x-axis; (ii) y-axisA)
B)
C)
D)
E)
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11
Match the graph with its polar equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
12
Find two sets of polar coordinates for the point for .
A)
B)
C)
D)
E)
for .A)
B)
C)
D)
E)
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13
Match the equation with its graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
Unlock Deck
k this deck
14
Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results.
A) eccentricity: distance from pole to directrix: The graph is an ellipse.
B) eccentricity: distance from pole to directrix: The graph is an ellipse.
C) eccentricity: distance from pole to directrix: The graph is an ellipse.
D) eccentricity: distance from pole to directrix: The graph is a hyperbola.
E) eccentricity: distance from pole to directrix: The graph is a hyperbola.
A) eccentricity:
distance from pole to directrix: The graph is an ellipse. B) eccentricity:
distance from pole to directrix: The graph is an ellipse. C) eccentricity:
distance from pole to directrix: The graph is an ellipse. D) eccentricity:
distance from pole to directrix: The graph is a hyperbola. E) eccentricity:
distance from pole to directrix: The graph is a hyperbola. Unlock Deck
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15
Identify the graph for the polar equation .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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k this deck
16
Match the equation with its graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
Unlock Deck
k this deck
17
Identify the graph for the polar equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
18
Match the graph with its polar equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
Unlock Deck
k this deck
19
Match the equation with its graph.
A)
B)
C)
D)
E) none of these
A)
B)
C)
D)
E) none of these
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
Unlock Deck
k this deck
20
Find two sets of polar coordinates for the point for .
A)
B)
C)
D)
E)
for .A)
B)
C)
D)
E)
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k this deck
21
Find a polar equation for the parabola with its focus at the pole and vertex .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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22
Find and if possible, and find the slope and concavity (if possible) at the point corresponding to t = 2.
A) : slope and concave up
B) slope 8 and concave down
C) slope 16 and concave up
D) : slope -8 and concave down
E) : slope and concave up
and if possible, and find the slope and concavity (if possible) at the point corresponding to t = 2. A)
: slope and concave upB)
slope 8 and concave downC)
slope 16 and concave upD)
: slope -8 and concave downE)
: slope and concave up Unlock Deck
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23
Find the center, foci, and vertices of the hyperbola.
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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24
Find the eccentricity of the polar equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
25
Find a polar equation for the hyperbola with its focus at the pole, eccentricity , and directrix .
A)
B)
C)
D)
E)
, and directrix .A)
B)
C)
D)
E)
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k this deck
26
Find the vertex of the parabola given by .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
27
Find the distance from the pole to the directrix for the conic .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Unlock Deck
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k this deck
28
Find the center of the ellipse given by .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
29
Find the area of the surface generated by revolving the curve about the x-axis on the interval .
A)
B)
C)
D)
E)
about the x-axis on the interval .A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
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k this deck
30
Identify the conic for the polar equation when .
A) ellipse
B) parabola
C) hyperbola
when .A) ellipse
B) parabola
C) hyperbola
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k this deck
31
Find and if possible, and find the slope and concavity (if possible) at the point corresponding to .
A) at : slope 1 and concave up
B) at : slope -1 and concave up
C) at : slope -1 and concave down
D) at : slope 1 and concave down
E) at : slope of -1 and concave up
and if possible, and find the slope and concavity (if possible) at the point corresponding to . A)
at : slope 1 and concave upB)
at : slope -1 and concave upC)
at : slope -1 and concave downD)
at : slope 1 and concave downE)
at : slope of -1 and concave up Unlock Deck
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k this deck
32
Find the second derivative of the parametric equations .
A)
B)
C)
D)
E)
of the parametric equations . A)
B)
C)
D)
E)
Unlock Deck
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k this deck
33
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
A) parabola
B) ellipse
C) circle
D) hyperbola
A) parabola
B) ellipse
C) circle
D) hyperbola
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k this deck
34
Find an equation of the hyperbola with vertices and asymptotes .
A)
B)
C)
D)
E)
and asymptotes .A)
B)
C)
D)
E)
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k this deck
35
Find an equation of the parabola with vertex and directrix .
A)
B)
C)
D)
E)
and directrix .A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
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k this deck
36
Find the length of the curve over the interval . Round your answer to two decimal places.
A) 0.58
B) 19.05
C) 11.00
D) 6.35
E) 1.73
over the interval . Round your answer to two decimal places. A) 0.58
B) 19.05
C) 11.00
D) 6.35
E) 1.73
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
Unlock Deck
k this deck
37
Convert the polar equation to rectangular form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
Unlock Deck
k this deck
38
Find a polar equation for the ellipse with its focus at the pole and vertices .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
39
Find a polar equation for the ellipse with its focus at the pole, eccentricity , and directrix .
A)
B)
C)
D)
E)
, and directrix .A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
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k this deck
40
Find all points (if any) of horizontal and vertical tangency to the curve .
A) horizontal tangents: , vertical tangents:
B) horizontal tangents: , vertical tangents:
C) horizontal tangent: , vertical tangent:
D) horizontal tangents: , vertical tangents:
E) horizontal tangent: , vertical tangent:
.A) horizontal tangents:
, vertical tangents: B) horizontal tangents:
, vertical tangents: C) horizontal tangent:
, vertical tangent: D) horizontal tangents:
, vertical tangents: E) horizontal tangent:
, vertical tangent: Unlock Deck
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41
Find the area of the surface generated by revolving the curve about the y-axis on the interval . Round your answer to two decimal places.
A) 1436.54
B) 1413.69
C) 1401.46
D) 706.85
E) 2132.77
about the y-axis on the interval . Round your answer to two decimal places. A) 1436.54
B) 1413.69
C) 1401.46
D) 706.85
E) 2132.77
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
Unlock Deck
k this deck
42
Find the arc length of the curve on the given interval.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
43
Find the arc length of the curve on the given interval.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
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k this deck
44
Determine the t intervals on which the curve is concave downward or concave upward.
A) concave downward: ; concave upward:
B) concave downward: ; concave upward:
C) concave downward:
D) concave upward:
E) concave downward:
is concave downward or concave upward.A) concave downward:
; concave upward: B) concave downward:
; concave upward: C) concave downward:
D) concave upward:
E) concave downward:
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
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k this deck
45
Use the result, "the set of parametric equations for the line passing through and is " to find a set of parametric equations for the line passing through and .
A)
B)
C)
D)
E)
and is " to find a set of parametric equations for the line passing through and .A)
B)
C)
D)
E)
Unlock Deck
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k this deck
46
The path of a projectile is modeled by the parametric equations and where x and y are measured in feet. Use a graphing utility to approximate the range of the projectile. Round your answer to two decimal places.
A) 335.33 ft
B) 558.88 ft
C) 73.76 ft
D) 419.16 ft
E) 209.58 ft
and where x and y are measured in feet. Use a graphing utility to approximate the range of the projectile. Round your answer to two decimal places.A) 335.33 ft
B) 558.88 ft
C) 73.76 ft
D) 419.16 ft
E) 209.58 ft
Unlock Deck
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k this deck
47
Find the center, foci, vertices, and eccentricity of the ellipse.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
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k this deck
48
Find a set of parametric equations for the rectangular equation that satisfies the condition at the point .
A)
B)
C)
D)
E)
that satisfies the condition at the point .A)
B)
C)
D)
E)
Unlock Deck
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k this deck
49
Convert the polar equation to rectangular form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 114 flashcards in this deck.
Unlock Deck
k this deck
50
Identify any points at which the cycloid is not smooth.
A) not smooth when
B) smooth everywhere
C) not smooth when
D) not smooth when
E) not smooth when
is not smooth.A) not smooth when
B) smooth everywhere
C) not smooth when
D) not smooth when
E) not smooth when
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k this deck
51
Find all points of intersection of the graphs of the equations.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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52
Write the corresponding rectangular equation for the curve represented by the parametric equations by eliminating the parameter.
A)
B)
C)
D)
E)
by eliminating the parameter.A)
B)
C)
D)
E)
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k this deck
53
Write the corresponding rectangular equation for the curve represented by the parametric equations by eliminating the parameter.
A)
B)
C)
D)
E)
by eliminating the parameter.A)
B)
C)
D)
E)
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k this deck
54
Find the area of inside and outside by sketching the graph of the equations using the graphing utility.
A)
B)
C)
D)
E)
and outside by sketching the graph of the equations using the graphing utility. A)
B)
C)
D)
E)
Unlock Deck
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55
Find the length of the curve over the given interval.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
56
Determine the t intervals on which the curve is concave downward or concave upward.
A) concave downward: ; concave upward:
B) concave downward: ; concave upward:
C) concave downward: ; concave upward:
D) concave downward: ; concave upward:
E) concave downward: ; concave upward:
is concave downward or concave upward.A) concave downward:
; concave upward: B) concave downward:
; concave upward: C) concave downward:
; concave upward: D) concave downward:
; concave upward: E) concave downward:
; concave upward: Unlock Deck
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57
Write the corresponding rectangular equation for the curve represented by the parametric equation by eliminating the parameter.
A)
B)
C)
D)
E)
by eliminating the parameter.A)
B)
C)
D)
E)
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k this deck
58
Find a set of parametric equations for the rectangular equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
59
Find the area of the surface formed by revolving about the axis the following curve over the given interval.
A)
B)
C)
D)
E)
axis the following curve over the given interval. A)
B)
C)
D)
E)
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k this deck
60
Sketch the curve represented by the parametric equations .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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k this deck
61
Find the arc length of the curve on the interval . Round your answer to three decimal places.
A) 287.453
B) 191.635
C) 193.606
D) 66.480
E) 99.721
on the interval . Round your answer to three decimal places.A) 287.453
B) 191.635
C) 193.606
D) 66.480
E) 99.721
Unlock Deck
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k this deck
62
Find a set of parametric equations for the rectangular equation that satisfies the condition at the point .
A)
B)
C)
D)
E)
that satisfies the condition at the point .A)
B)
C)
D)
E)
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k this deck
63
Find the area of the region lying between the loops of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
64
Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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65
Find the area of the inner loop of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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k this deck
66
Find the area of the surface generated by revolving the curve about the given axis. (i) x-axis; (ii) y-axis
A)
B)
C)
D)
E)
(i) x-axis; (ii) y-axisA)
B)
C)
D)
E)
Unlock Deck
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k this deck
67
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
A) parabola
B) circle
C) ellipse
D) hyperbola
A) parabola
B) circle
C) ellipse
D) hyperbola
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68
Find the foci of the ellipse given by .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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k this deck
69
Use the result, "the set of parametric equations for the ellipse is " to find a set of parametric equations for the ellipse with vertices and and with foci at and .
A)
B)
C)
D)
E)
" to find a set of parametric equations for the ellipse with vertices and and with foci at and . A)
B)
C)
D)
E)
Unlock Deck
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k this deck
70
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
A) circle
B) hyperbola
C) ellipse
D) parabola
A) circle
B) hyperbola
C) ellipse
D) parabola
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71
Identify any points at which the Folium of Descartes is not smooth. Round your answer to two decimal places, if necessary.
A) not smooth when
B) not smooth when
C) not smooth when
D) smooth everywhere
E) not smooth when
is not smooth. Round your answer to two decimal places, if necessary.A) not smooth when
B) not smooth when
C) not smooth when
D) smooth everywhere
E) not smooth when
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72
Find the distance from the pole to the directrix for the conic .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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73
Uranus moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 2,876,769,540 kilometers, and the eccentricity is 0.0444. Find the minimum distance (perihelion) of Uranus from the sun. Round your answer to nearest kilometer.
A) 3,004,498,108 km
B) 2,749,040,972 km
C) 2,819,234,149 km
D) 7,819,870,365 km
E) 2,934,304,931 km
A) 3,004,498,108 km
B) 2,749,040,972 km
C) 2,819,234,149 km
D) 7,819,870,365 km
E) 2,934,304,931 km
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k this deck
74
Find the distance from the pole to the directrix for the conic .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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k this deck
75
Find the eccentricity of the polar equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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k this deck
76
Find the vertex, focus, and directrix of the parabola and sketch its graph.
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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77
Find the area of one petal of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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k this deck
78
The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle with the horizontal and having an initial velocity of feet per second is given by and . The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of degrees with the horizontal at a speed of 95 miles per hour as shown in the figure. Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run using the parametric equations and . Round your answer to one decimal place.
A)
B)
C)
D)
E)
with the horizontal and having an initial velocity of feet per second is given by and . The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of degrees with the horizontal at a speed of 95 miles per hour as shown in the figure. Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run using the parametric equations and . Round your answer to one decimal place. A)
B)
C)
D)
E)
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79
Find the area of the interior of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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80
For the given point in polar coordinates, find the corresponding rectangular coordinates for the point. .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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Unlock Deck
Unlock for access to all 114 flashcards in this deck.
