Deck 9: Analytic Geometry

Question 1

Find an equation of the parabola described and state the two points that define the latus rectum.

Answer 1

C

Question 2

Match the equation to its graph.

Answer 2

A

Question 3

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

Answer 3

D

Question 4

Match the equation to its graph.

Question 5

Name the conic.

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

Question 6

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

Question 7

Find an equation of the parabola described.
Focus at (0, 21); directrix the line y = -21

Question 8

Graph the equation.

Question 9

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

Question 10

Find an equation of the parabola described.
Focus at (-3, 0); directrix the line x = 3

Question 11

Match the equation to its graph.

Question 12

Name the conic.

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

Question 13

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

Question 14

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

Question 15

Graph the equation.

Question 16

Graph the equation.

Question 17

Vertex at (0, 0); axis of symmetry the x-axis; containing the point (9, 5)

Question 18

Name the conic.

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

Question 19

Match the equation to its graph.

Question 20

Name the conic.

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

Question 21

Find an equation for the parabola described.

Question 22

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

Question 23

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

Question 24

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

Question 25

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

Question 26

Find an equation for the parabola described.

Question 27

Write an equation for the parabola.

Question 28

Graph the equation.

Question 29

Find an equation for the parabola described.

Question 30

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

Question 31

Find an equation for the parabola described.

Question 32

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

Question 33

Write an equation for the parabola.

Question 34

Match the equation to the graph.

Question 35

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

Question 36

Graph the equation.

Question 37

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

Question 38

Match the equation to the graph.

Question 39

Match the equation to the graph.

Question 40

Match the equation to the graph.

Question 41

Solve the problem.
A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 24 inches across at its opening and is 4 feet deep, where will the light be concentrated?

A) 0.1 in. from the vertex
B) 10.1 in. from the vertex
C) 0.2 in. from the vertex
D) 0.8 in. from the vertex

Question 42

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

Question 43

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 the focus, is
3 centimeters from the vertex. If the depth is to be 6 centimeters, what is the diameter of the headlight at its
opening?

Question 44

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

Question 45

Choose the one alternative that best completes the 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. How far from the vertex is the focus? Round answer to two decimal places.

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

Question 46

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

Question 47

Solve the problem.

Question 48

Solve the problem.
A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 174 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center.

A) 3.6 ft
B) 21.8 ft
C) 0.2 ft
D) 29.1 ft

Question 49

Find an equation for the ellipse described.

Question 50

Match the graph to its equation.

Question 51

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 top of a second
Tower. The towers stand 50 inches apart. At a point between the towers and 15 inches along the road from the
Base of one tower, the cable is 1 inches above the roadway. Find the height of the towers.

A) 6.75 in.
B) 5.75 in.
C) 6.25 in.
D) 8.25 in.

Question 52

Graph the equation.

Question 53

Match the graph to its equation.

Question 54

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 top of a second
Tower. The towers are both 12.25 inches tall and stand 70 inches apart. Find the vertical distance from the
Roadway to the cable at a point on the road 14 inches from the lowest point of the cable.

A) 2.16 in.
B) 1.76 in.
C) 7.84 in.
D) 1.96 in.

Question 55

Graph the equation.

Question 56

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 top of a second
Tower. The towers are both 12.25 inches tall and stand 70 inches apart. At some point along the road from the
Lowest point of the cable, the cable is 1.96 inches above the roadway. Find the distance between that point and
The base of the nearest tower.

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

Question 57

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

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

Question 58

Graph the equation.

Question 59

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 strike the
surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 8 feet across at
its opening and is 2 feet deep at its center, at what position should the receiver be placed?

Question 60

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

Question 61

Find an equation for the ellipse described.

Question 62

Graph the ellipse and locate the foci.

Question 63

Find an equation for the ellipse described.

Question 64

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

Question 65

Write an equation for the graph.

Question 66

Find an equation for the ellipse described.

Question 67

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

Question 68

Find an equation for the ellipse described.

Question 69

Find an equation for the ellipse described.

Question 70

Find an equation for the ellipse described.

Question 71

Graph the ellipse and locate the foci.

Question 72

Find an equation for the ellipse described.

Question 73

Find an equation for the ellipse described.

Question 74

Graph the ellipse and locate the foci.

Question 75

Graph the ellipse and locate the foci.

Question 76

Find an equation for the ellipse described.

Question 77

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

Question 78

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

Question 79

Find an equation for the ellipse described.

Question 80

Find an equation for the ellipse described.