# Quiz 11: Topics From Analytic Geometry

Mathematics

Free

Multiple Choice

B

Q 2Q 2

Find an equation of the parabola that satisfies the condition. Focus , directrix
A)
B)
C)
D)
E)

Free

Multiple Choice

A

Q 3Q 3

Find an equation of the parabola that satisfies the condition. Vertex , directrix
A)
B)
C)
D)
E)

Free

Multiple Choice

B

Free

Multiple Choice

Q 5Q 5

Find an equation of the parabola that satisfies the given conditions. Vertex at the origin, symmetric to the y-axis, and passing through the point ( 4, 7 )
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

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Q 8Q 8

Find an equation for the ellipse that has its center at the origin and satisfies the conditions.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 9Q 9

Find an equation for the set of points in an xy-plane such that the sum of the distances from and is .
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 10Q 10

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 11Q 11

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 12Q 12

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 13Q 13

Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 14Q 14

Find an equation for the set of points in an xy-plane such that the difference of the distances from F and F ' is k.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 15Q 15

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C, and indicate the orientation. t in
A)
D)
B)
E)
C)

Free

Multiple Choice

Free

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Q 17Q 17

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C. -1 t 1
A)
C)
B)
D)

Free

Multiple Choice

Q 18Q 18

The parametric equations specify the position of a moving point P ( x, y ) at time t. Sketch the graph.
A)
C)
B)
D)

Free

Multiple Choice

Q 19Q 19

Lissajous figures are used in the study of electrical circuits to determine the phase difference between a known voltage and an unknown voltage having the same frequency. The voltages are graphed parametrically as and . If is acute, then where y

_{ }_{int}_{ }is the nonnegative y -intercept and y_{ max }is the maximum y-value on the curve. Graph the parametric curve and use the graph to approximate in degrees if A) B) C) D) E)Free

Multiple Choice

Free

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Free

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Free

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Free

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Q 24Q 24

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 25Q 25

Polar equations of conics can be used to describe the motion of comets. These paths can be graphed using the following polar equation, where e is the eccentricity of the conic and r

_{ per }is the perihelion distance measured in AU. The orbit of Saturn has r_{ per }= 9.006 and e = 0.056. The motion of Encke's Comet has r_{ per }= 0.3317 and e = 2.718282. Graph both the motion of the comet and the orbit of Saturn. A) C) B) D)Free

Multiple Choice

Free

Multiple Choice

Q 27Q 27

Find an equation of the parabola that satisfies the condition. Focus , directrix
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 28Q 28

Find an equation of the parabola that satisfies the condition. Vertex , directrix
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 29Q 29

Find an equation of the parabola that satisfies the condition. Vertex , focus
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 30Q 30

Find an equation of the parabola that satisfies the given conditions. Vertex at the origin, symmetric to the y-axis, and passing through the point ( 5, 8 )
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

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Free

Multiple Choice

Q 33Q 33

Find an equation for the ellipse that has its center at the origin and satisfies the conditions.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 34Q 34

Find an equation for the set of points in an xy-plane such that the sum of the distances from and is .
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 35Q 35

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 36Q 36

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 37Q 37

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 38Q 38

Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 39Q 39

Find an equation for the set of points in an xy-plane such that the difference of the distances from F and F ' is k.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 40Q 40

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C, and indicate the orientation. t in
A)
D)
B)
E)
C)

Free

Multiple Choice

Free

Multiple Choice

Q 42Q 42

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C. -1 t 1
A)
C)
B)
D)

Free

Multiple Choice

Q 43Q 43

The parametric equations specify the position of a moving point P ( x, y ) at time t. Sketch the graph.
A)
C)
B)
D)

Free

Multiple Choice

Q 44Q 44

Lissajous figures are used in the study of electrical circuits to determine the phase difference between a known voltage and an unknown voltage having the same frequency. The voltages are graphed parametrically as and . If is acute, then where y

_{ }_{int}_{ }is the nonnegative y -intercept and y_{ max }is the maximum y-value on the curve. Graph the parametric curve and use the graph to approximate in degrees if A) B) C) D) E)Free

Multiple Choice

Free

Multiple Choice

Free

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Free

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Free

Multiple Choice

Q 49Q 49

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 50Q 50

Polar equations of conics can be used to describe the motion of comets. These paths can be graphed using the following polar equation, where e is the eccentricity of the conic and r

_{ per }is the perihelion distance measured in AU. The orbit of Saturn has r_{ per }= 9.006 and e = 0.056. The motion of Comet 1973.99 has r_{ per }= 0.142 and e = 2.718282. Graph both the motion of the comet and the orbit of Saturn. A) C) B) D)Free

Multiple Choice

Free

Multiple Choice

Q 52Q 52

Find an equation of the parabola that satisfies the condition. Focus , directrix
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 53Q 53

Find an equation of the parabola that satisfies the condition. Vertex , directrix
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 54Q 54

Find an equation of the parabola that satisfies the condition. Vertex , focus
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 55Q 55

Find an equation of the parabola that satisfies the given conditions. Vertex at the origin, symmetric to the y-axis, and passing through the point ( 2, 5 )
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 58Q 58

Find an equation for the ellipse that has its center at the origin and satisfies the conditions.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 59Q 59

Find an equation for the set of points in an xy-plane such that the sum of the distances from and is .
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 60Q 60

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 61Q 61

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 62Q 62

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 63Q 63

Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 64Q 64

Find an equation for the set of points in an xy-plane such that the difference of the distances from F and F ' is k.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 65Q 65

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C, and indicate the orientation. t in
A)
D)
B)
E)
C)

Free

Multiple Choice

Free

Multiple Choice

Q 67Q 67

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C. -1 t 1
A)
C)
B)
D)

Free

Multiple Choice

Q 68Q 68

The parametric equations specify the position of a moving point P ( x, y ) at time t. Sketch the graph.
A)
C)
B)
D)

Free

Multiple Choice

Q 69Q 69

Lissajous figures are used in the study of electrical circuits to determine the phase difference between a known voltage and an unknown voltage having the same frequency. The voltages are graphed parametrically as and . If is acute, then where y

_{ }_{int}_{ }is the nonnegative y -intercept and y_{ max }is the maximum y-value on the curve. Graph the parametric curve and use the graph to approximate in degrees if A) B) C) D) E)Free

Multiple Choice

Free

Multiple Choice

Free

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Free

Multiple Choice

Free

Multiple Choice

Q 74Q 74

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 75Q 75

Polar equations of conics can be used to describe the motion of comets. These paths can be graphed using the following polar equation, where e is the eccentricity of the conic and r

_{ per }is the perihelion distance measured in AU. The orbit of Saturn has r_{ per }= 9.006 and e = 0.056. The motion of Comet 1973.99 has r_{ per }= 0.142 and e = 2.718282. Graph both the motion of the comet and the orbit of Saturn. A) C) B) D)Free

Multiple Choice

Q 76Q 76

Find an equation of the parabola that satisfies the condition. Vertex , focus
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 77Q 77

Find an equation for the set of points in an xy-plane that are equidistant from the point P and the line l.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 78Q 78

Find an equation for the parabola that has a horizontal axis and passes through the given points.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

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Free

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Free

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Free

Multiple Choice

Q 83Q 83Find an equation for the ellipse that has its center at the origin and satisfies the conditions.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 84Q 84

An arch of a bridge is semi-elliptical, with major axis horizontal. The base of the arch is 30 feet across, and the highest part of the arch is 10 feet above the horizontal roadway, as shown in the figure. Find the height of the arch 7 feet from the center of the base.
A)8.8 ft
B)7.3 ft
C)17.7 ft
D)11.0 ft
E)12.1 ft

Free

Multiple Choice

Q 85Q 85

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola.
A)Parabola with horizontal axis
B)Circle
C)Ellipse
D)Hyperbola
E)Parabola with vertical axis

Free

Multiple Choice

Free

Multiple Choice

Q 87Q 87

Shown in the figure is the Lissajous figure given by Find the period of the figure - that is, the length of the smallest t-interval that traces the curve.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 88Q 88

Lissajous figures are used in the study of electrical circuits to determine the phase difference between a known voltage and an unknown voltage having the same frequency. The voltages are graphed parametrically as and . If is acute, then where y

_{ }_{int}_{ }is the nonnegative y -intercept and y_{ max }is the maximum y -value on the curve. Graph the parametric curve and use the graph to approximate in degrees if A) B) C) D) E)Free

Multiple Choice

Q 89Q 89

Find a polar equation in r and that has the same graph as the equation in x and y.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 90Q 90

Find a polar equation in r and that has the same graph as the equation in x and y.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 91Q 91

Find a polar equation in r and that has the same graph as the equation in x and y.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

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Free

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Free

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Free

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Q 96Q 96Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 97Q 97Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 98Q 98

Find a polar equation in r and of the parabola with focus at the pole and the given vertex.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 99Q 99

Find a polar equation in r and of the parabola with focus at the pole and the given vertex.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 100Q 100

Polar equations of conics can be used to describe the motion of comets. These paths can be graphed using the following polar equation, where e is the eccentricity of the conic and r

_{ per }is the perihelion distance measured in AU. For Encke's Comet r_{ per }= 0.3317 and e = 0.8499, determine whether its trajectory is elliptical, parabolic, or hyperbolic. A)parabolic B)hyperbolic C)ellipticalFree

Multiple Choice

Q 101Q 101

Find an equation of the parabola that satisfies the condition. Vertex , focus
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 102Q 102

Find an equation for the set of points in an xy-plane that are equidistant from the point P and the line l.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 103Q 103

Find an equation for the parabola that has a horizontal axis and passes through the given points.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 108Q 108Find an equation for the ellipse that has its center at the origin and satisfies the conditions.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 109Q 109

An arch of a bridge is semi-elliptical, with major axis horizontal. The base of the arch is 30 feet across, and the highest part of the arch is 10 feet above the horizontal roadway, as shown in the figure. Find the height of the arch 7 feet from the center of the base.
A)11.0 ft
B)17.7 ft
C)8.8 ft
D)12.1 ft
E)7.3 ft

Free

Multiple Choice

Q 110Q 110

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola.
A)Hyperbola
B)Circle
C)Parabola with horizontal axis
D)Ellipse
E)Parabola with vertical axis

Free

Multiple Choice

Free

Multiple Choice

Q 112Q 112

Shown in the figure is the Lissajous figure given by Find the period of the figure - that is, the length of the smallest t-interval that traces the curve.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 113Q 113

Lissajous figures are used in the study of electrical circuits to determine the phase difference between a known voltage and an unknown voltage having the same frequency. The voltages are graphed parametrically as and . If is acute, then where y

_{ }_{int}_{ }is the nonnegative y -intercept and y_{ max }is the maximum y -value on the curve. Graph the parametric curve and use the graph to approximate in degrees if A) B) C) D) E)Free

Multiple Choice

Q 114Q 114

Find a polar equation in r and that has the same graph as the equation in x and y.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 115Q 115

Find a polar equation in r and that has the same graph as the equation in x and y.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 116Q 116

Find a polar equation in r and that has the same graph as the equation in x and y.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

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Free

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Free

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Free

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Q 121Q 121Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 122Q 122Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 123Q 123

Find a polar equation in r and of the parabola with focus at the pole and the given vertex.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 124Q 124Find a polar equation in r and of the parabola with focus at the pole and the given vertex.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 125Q 125

Polar equations of conics can be used to describe the motion of comets. These paths can be graphed using the following polar equation, where e is the eccentricity of the conic and r

_{ per }is the perihelion distance measured in AU. For Comet 1973.99 r_{ per }= 0.142 and e = 1.000, determine whether its trajectory is elliptical, parabolic, or hyperbolic. A)elliptical B)hyperbolic C)parabolicFree

Multiple Choice

Q 126Q 126

Find an equation of the parabola that satisfies the condition. Vertex , focus
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 127Q 127

Find an equation for the set of points in an xy-plane that are equidistant from the point P and the line l.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 128Q 128

Find an equation for the parabola that has a horizontal axis and passes through the given points.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 133Q 133Find an equation for the ellipse that has its center at the origin and satisfies the conditions.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 134Q 134

An arch of a bridge is semi-elliptical, with major axis horizontal. The base of the arch is 30 feet across, and the highest part of the arch is 10 feet above the horizontal roadway, as shown in the figure. Find the height of the arch 7 feet from the center of the base.
A)12.1 ft
B)8.8 ft
C)17.7 ft
D)11.0 ft
E)7.3 ft

Free

Multiple Choice

Q 135Q 135

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola.
A)Parabola with vertical axis
B)Hyperbola
C)Ellipse
D)Parabola with horizontal axis
E)Circle

Free

Multiple Choice

Free

Multiple Choice

Q 137Q 137

Shown in the figure is the Lissajous figure given by Find the period of the figure - that is, the length of the smallest t-interval that traces the curve.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 138Q 138

Lissajous figures are used in the study of electrical circuits to determine the phase difference between a known voltage and an unknown voltage having the same frequency. The voltages are graphed parametrically as and . If is acute, then where y

_{ }_{int}_{ }is the nonnegative y -intercept and y_{ max }is the maximum y -value on the curve. Graph the parametric curve and use the graph to approximate in degrees if A) B) C) D) E)Free

Multiple Choice

Q 139Q 139

Find a polar equation in r and that has the same graph as the equation in x and y.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 140Q 140

Find a polar equation in r and that has the same graph as the equation in x and y.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 141Q 141

Find a polar equation in r and that has the same graph as the equation in x and y.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Free

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Free

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Free

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Q 146Q 146Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 147Q 147Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 148Q 148Find a polar equation in r and of the parabola with focus at the pole and the given vertex.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 149Q 149Find a polar equation in r and of the parabola with focus at the pole and the given vertex.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 150Q 150

Polar equations of conics can be used to describe the motion of comets. These paths can be graphed using the following polar equation, where e is the eccentricity of the conic and r

_{ per }is the perihelion distance measured in AU. For Encke's Comet r_{ per }= 0.3317 and e = 0.8499, determine whether its trajectory is elliptical, parabolic, or hyperbolic. A)parabolic B)elliptical C)hyperbolicFree

Multiple Choice