Deck 7: Analytic Geometry

Question 1

Find an equation of the parabola described.
Focus at (0, 11); directrix the line y = -11

A)
B)
C)
D)

Answer 1

Question 2

Find an equation of the parabola described.
Focus at (4, 0); vertex at (0, 0)

A)
B)
C)
D)

Answer 2

Question 3

Find the vertex, focus, and directrix of the parabola. Graph the equation.

A)vertex: (0, 0)
focus: (0, -4)
directrix: y = 4

B)vertex: (0, 0)
focus: (0, 4)
directrix: y = -4

C)vertex: (0, 0)
focus: (-4, 0)
directrix: x = 4

D)vertex: (0, 0)
focus: (4, 0)
directrix: x = -4

Answer 3

vertex: (0, 0)
focus: (0, -4)
directrix: y = 4

Question 4

Graph the equation.

A)
B)
C)
D)

Question 5

Graph the equation.

A)
B)
C)
D)

Question 6

Match the equation to its graph.

A)
B)
C)
D)

Question 7

Match the equation to its graph.

A)
B)
C)
D)

Question 8

Match the equation to its graph.

A)
B)
C)
D)

Question 9

Find an equation of the parabola described.
Directrix the line y = 3; vertex at (0, 0)

A)
B)
C)
D)

Question 10

Find the vertex, focus, and directrix of the parabola. Graph the equation.

A)vertex: (0, 0)
focus: (0, -4)
directrix: y = 4

B) vertex: (0, 0)
focus: (0, 4)
directrix: y = -4

C)vertex: (0, 0)
focus: (-4, 0)
directrix: x = 4

D)vertex: (0, 0)
focus: (4, 0)
directrix: x = -4

Question 11

Name the conic.

A)hyperbola
B)circle
C)ellipse
D)parabola

Question 12

Name the conic.

A)circle
B)ellipse
C)parabola
D)hyperbola

Question 13

Graph the equation.

A)
B)
C)
D)

Question 14

Match the equation to its graph.

A)
B)
C)
D)

Question 15

Find an equation of the parabola described.
Focus at (11, 0); directrix the line x = -11

A)
B)
C)
D)

Question 16

Name the conic.

A)ellipse
B)circle
C)parabola
D)hyperbola

Question 17

Name the conic.

A)parabola
B)circle
C)ellipse
D)hyperbola

Question 18

Find an equation of the parabola described.
Vertex at (0, 0); axis of symmetry the x-axis; containing the point (1, 3)

A)
B)
C)
D)

Question 19

Find an equation of the parabola described.
Focus at (5, 0); vertex at (0, 0)

A)
B)
C)
D)

Question 20

Find an equation of the parabola described and state the two points that define the latus rectum.
Focus at (0, 3); directrix the line y = -3

A) latus rectum: (6, 3)and (-6, 3)
B) latus rectum: (7, 8)and (-7, 8)
C) latus rectum: (3, 6)and (-3, 6)
D) latus rectum: (8, 3)and (-8, 3)

Question 21

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

A)vertex: (-4, 1)focus: (-4, 0)directrix: y = 2
B)vertex: (4, -1)focus: (4, -2)directrix: y = 0
C)vertex: (1, -4)focus: (1, -5)directrix: y = -3
D)vertex: (-4, 1)focus: (-4, 2)directrix: x = 0

Question 22

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

A)vertex: (-2, 1)focus: (-2, 5)directrix: y = -3
B)vertex: (2, -1)focus: (2, 3)directrix: y = -5
C)vertex: (1, -2)focus: (1, 2)directrix: y = -6
D)vertex: (-2, 1)focus: (-2, -3)directrix: x = 5

Question 23

Find an equation for the parabola described.
Vertex at (4, 8); focus at (4, 6)

A)
B)
C)
D)

Question 24

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

A)vertex: (3, 2)focus: (6, 2)directrix: x = 0
B)vertex: (-3, -2)focus: (0, -2)directrix: x = -6
C)vertex: (2, 3)focus: (5, 3)directrix: x = -1
D)vertex: (3, 2)focus: (0, 2)directrix: x = 6

Question 25

Graph the equation.

A)
B)
C)
D)

Question 26

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

A)vertex: (2, -3)focus: (1, -3)directrix: x = 3
B)vertex: (-2, 3)focus: (-3, 3)directrix: x = -1
C)vertex: (-3, 2)focus: (-4, 2)directrix: x = -2
D)vertex: (2, -3)focus: (3, -3)directrix: x = 1

Question 27

Graph the equation.

A)
B)
C)
D)

Question 28

Find the vertex, focus, and directrix of the parabola. Graph the equation.

A)vertex: (1, -1)focus: (1, 0)directrix: y = -2
B)vertex: (-1, 1)focus: (-1, 2)directrix: y = 0
C)vertex: (1, -1)focus: (2, -1)directrix: x = 0
D)vertex: (-1, 1)focus: (0, 1)directrix: x = -2

Question 29

Find the vertex, focus, and directrix of the parabola. Graph the equation.

A)vertex: (3, 6)focus: (3, 7)directrix: y = 5
B)vertex: (3, 6)focus: (3, 5)directrix: y = 7
C)vertex: (3, 6)focus: (4, 6)directrix: x = 2
D)vertex: (3, 6)focus: (2, 6)directrix: x = 4

Question 30

Find an equation for the parabola described.
Vertex at (7, -3); focus at (9, -3)

A)
B)
C)
D)

Question 31

Find an equation for the parabola described.
Vertex at (3, -8); focus at (3, -9)

A)
B)
C)
D)

Question 32

Write an equation for the parabola.

A)
B)
C)
D)

Question 33

Match the equation to the graph.

A)
B)
C)
D)

Question 34

Match the equation to the graph.

A)
B)
C)
D)

Question 35

Find the vertex, focus, and directrix of the parabola. Graph the equation.

A)vertex: (-7, -4)focus: (-5, -4)directrix: x = -9
B)vertex: (-7, -4)focus: (-9, -4)directrix: x = -5
C)vertex: (-7, -4)focus: (-7, -2)directrix: y = -6
D)vertex: (-7, -4)focus: (-7, -6)directrix: y = -2

Question 36

Find the vertex, focus, and directrix of the parabola. Graph the equation.

A)vertex: (-2, -2)focus: (-1.75, -2)directrix: x = -2.25
B)vertex: (2, 2)focus: (2.25, 2)directrix: x = 1.75
C)vertex: (-2, -2)focus: (-2, -1.75)directrix: y = -2.25
D)vertex: (2, 2)focus: (2, 2.25)directrix: y = 1.75

Question 37

Write an equation for the parabola.

A)
B)
C)
D)

Question 38

Find an equation for the parabola described.
Vertex at (4, 3); focus at (7, 3)

A)
B)
C)
D)

Question 39

Match the equation to the graph.

A)
B)
C)
D)

Question 40

Match the equation to the graph.

A)
B)
C)
D)

Question 41

Match the graph to its equation.

A)
B)
C)
D)

Question 42

Solve the problem.
A searchlight is shaped like a paraboloid of revolution. If the light source is located 5 feet from the basealong the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?

A)0.8 ft
B)1.6 ft
C)3.2 ft
D)4 ft

Question 43

Solve the problem.
An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section,cable runs from the top of one tower down to the roadway, just touching it there, and up again to the topof a second tower. The towers are both 12.25 inches tall and stand 70 inches apart. At some point along theroad from the lowest point of the cable, the cable is 1.96 inches above the roadway. Find the distancebetween that point and the base of the nearest tower.

A)21 in.
B)13.8 in.
C)21.2 in.
D)14.2 in.

Question 44

Solve the problem.
A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex tothe focus is 25 feet and the distance across the top of the mirror is 62 inches, how deep is the mirror in thecenter?

A)
B)
C)
D)

Question 45

Find the center, foci, and vertices of the ellipse.

A)center at (0, 0)foci at vertices at (0, -6), (0, 6)
B)center at (0, 0)foci at vertices at (-6, 0), (6, 0)
C)center at (0, 0)foci at (0, -6)and (0, 6)vertices at (0, -36), (0, 36)
D)center at (0, 0)foci at (0, 6)and (2, 0)vertices at (0, 36)and (4, 0)

Question 46

Graph the equation.

A)
B)
C)
D)

Question 47

Solve the problem.
An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section,cable runs from the top of one tower down to the roadway, just touching it there, and up again to the topof a second tower. The towers stand 40 inches apart. At a point between the towers and 12 inches along theroad from the base of one tower, the cable is 0.64 inches above the roadway. Find the height of the towers.

A)4 in.
B)4.5 in.
C)3.5 in.
D)6 in.

Question 48

Find an equation for the ellipse described.
Center at (0, 0); focus at (5, 0); vertex at (6, 0)

A)
B)
C)
D)

Question 49

Match the graph to its equation.

A)
B)
C)
D)

Question 50

Write the word or phrase that best completes each statement or answers the question.
A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. Howfar from the vertex is the focus? Round answer to two decimal places.

A)0.90 ft
B)0.52 ft
C)0.21 ft
D)0.26 ft

Question 51

Write the word or phrase that best completes each statement or answers the question.
A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strikethe surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 8 feetacross at its opening and is 2 feet deep at its center, at what position should the receiver be placed?

Question 52

Find the center, foci, and vertices of the ellipse.

A)center at (0, 0)foci at vertices at (0, -6), (0, 6)
B)center at (0, 0)foci at vertices at (-6, 0), (6, 0)
C)center at (0, 0)foci at (0, -6)and (0, 6)vertices at (0, -36), (0, 36)
D)center at (0, 0)foci at (0, 6)and (4, 0)vertices at (0, 36), (16, 0)

Question 53

Solve the problem.
A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 158 feet and a maximumheight of 30 feet. Find the height of the arch at 10 feet from its center.

A)29.5 ft
B)0.1 ft
C)1.9 ft
D)8.8 ft

Question 54

Graph the equation.

A)
B)
C)
D)

Question 55

Write the word or phrase that best completes each statement or answers the question.
A sealed-beam headlight is in the shape of a paraboloid of revolution. The bulb, which is placed at thefocus, is 3 centimeters from the vertex. If the depth is to be 6 centimeters, what is the diameter of theheadlight at its opening?

Question 56

Find the center, foci, and vertices of the ellipse.

A)center at (0, 0)foci at vertices at (-7, 0), (7, 0)
B)center at (0, 0)foci at vertices at (0, -7), (0, 7)
C)center at (0, 0)foci at (-7, 0)and (7, 0)vertices at (-49, 0), (49, 0)
D)center at (0, 0)foci at (0, -4)and (0, 4)vertices at (0, -16), (0, 16)

Question 57

Solve the problem.
A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 16 inchesacross at its opening and is 5 feet deep, where will the light be concentrated?

A)0.3 in. from the vertex
B)3.2 in. from the vertex
C)1.6 in. from the vertex
D)0.8 in. from the vertex

Question 58

Graph the equation.

A)
B)
C)
D)

Question 59

Solve the problem.
An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section,cable runs from the top of one tower down to the roadway, just touching it there, and up again to the topof a second tower. The towers are both 6.25 inches tall and stand 50 inches apart. Find the vertical distancefrom the roadway to the cable at a point on the road 10 inches from the lowest point of the cable.

A)1 in.
B)4 in.
C)1.2 in.
D)0.8 in.

Question 60

Find the center, foci, and vertices of the ellipse.

A)center at (0, 0)foci at vertices at (-9, 0), (9, 0)
B)center at (0, 0)foci at vertices at (0, -9), (0, 9)
C)center at (0, 0)foci at (-9, 0)and (9, 0)vertices at (-81, 0), (81, 0)
D)center at (0, 0)foci at (0, -6)and (0, 6)vertices at (0, -36), (0, 36)

Question 61

Find an equation for the ellipse described.
Focus at (-2, 0); vertices at

A)
B)
C)
D)

Question 62

Graph the equation.

A)
B)
C)
D)

Question 63

Find an equation for the ellipse described.
Center at (0, 0); focus at (0, 3); vertex at (0, -6)

A)
B)
C)
D)

Question 64

Graph the equation.

A)
B)
C)
D)

Question 65

Graph the equation.

A)
B)
C)
D)

Question 66

Graph the ellipse and locate the foci.

A)
B)
C)
D)

Question 67

Find the center, foci, and vertices of the ellipse.

A)
B)
C)
D)

Question 68

Graph the ellipse and locate the foci.

A)
B)
C)
D)f

Question 69

Find an equation for the ellipse described.
Center (0, 0); major axis horizontal with length 12; length of minor axis is 8

A)
B)
C)
D)

Question 70

Graph the ellipse and locate the foci.

A)
B)
C)
D)

Question 71

Find the center, foci, and vertices of the ellipse.

A)center at (2, -2)foci at ( vertices at (-2, -2), (6, -2)
B)center at (-2, 2)foci at vertices at (-2, -2), (6, -2)
C)center at (2, -2)foci at vertices at (4, -2), (-4, -2)
D)center at (2, -2)foci at vertices at (4, -2), (-4, -2)

Question 72

Find an equation for the ellipse described.
Center at (5, 3); focus at (12, 3); vertex at (14, 3)

A)
B)
C)
D)

Question 73

Graph the equation.

A)
B)
C)
D)

Question 74

Write an equation for the graph.

A)
B)
C)
D

Question 75

Find the center, foci, and vertices of the ellipse.
1 + 9(y + 3)2 = 144

A)center at (2, -3)foci at vertices at (2, 1), (2, -7)
B)center at (-3, 2)foci at vertices at (-3, 1), (-3, -7)
C)center at (-2, -3)foci at vertices at (-2, 1), (-2, -7)
D)center at (3, -3)foci at vertices at (3, 1), (3, -7)

Question 76

Find the center, foci, and vertices of the ellipse.

A) center: (5, -7); foci: (6.4, -7), (3.6, -7); vertices: (7.2, -7), (2.8, -7)
B) center: (5, -7); foci: (6.4, -7), (3.6, -7); vertices: (7.2, -7), (2.8, -7)
C) center: (-5, 7); foci: (-3.6, 7), (-6.4, 7); vertices: (-7.2, 7), (-2.8, 7)
D) center: (-5, 7); foci: (-3.6, 7), (-6.4, 7); vertices: (-7.2, 7), (-2.8, 7)

Question 77

Find an equation for the ellipse described.
Foci at x-intercepts are

A)
B)
C)
D)

Question 78

Find an equation for the ellipse described.
Center at (0, 0); focus at (-4, 0); vertex at (5, 0)

A)
B)
C)
D)

Question 79

Find an equation for the ellipse described.
Center at (0, 0); focus at (0, 5); vertex at (0, 7)

A)
B)
C)
D)

Question 80

Graph the ellipse and locate the foci.

A)
B)
C)
D)