Deck 14: Conic Sections

Question 1

Write the equation in the form y and then graph the equation.

A)
B)
C)
D)

Answer 1

Question 2

Determine whether the graph of the quadratic function opens up or down.

A) up
B) down

Answer 2

up

Question 3

Determine whether the graph of the quadratic function opens up or down.

A) up
B) down

Answer 3

up

Question 4

Name the conic.

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

Question 5

Graph the equation.

A)
B)
C)
D)

Question 6

Write the equation in the form y and then graph the equation.

A)
B)
C)
D)

Question 7

Write the equation in the form y and then graph the equation.

A)
B)
C)
D)

Question 8

Write the equation in the form y and then graph the equation.

A)
B)
C)
D)

Question 9

Name the conic.

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

Question 10

Name the conic.

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

Question 11

Graph the equation.

A)
B)
C)
D)

Question 12

Graph the equation.

A)
B)
C)
D)

Question 13

Write the equation in the form

A) y = (x + 7)2 + 50
B)
C)
D)

Question 14

Graph the equation.

A)
B)
C)
D)

Question 15

Write the equation in the form y and then graph the equation.

A)
B)
C)
D)

Question 16

Write the equation in the form y and then graph the equation.
x

A)
B)
C)
D)

Question 17

Graph the equation.

A)
B)
C)
D)

Question 18

Graph the equation.

A)
B)
C)
D)

Question 19

Name the conic.

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

Question 20

Write the equation in the form y and then graph the equation.

A)
B)
C)
D)

Question 21

Write the equation in the form y and then graph the equation.

A)
B)
C)
D)

Question 22

Write the equation of the circle with the given center and radius.
Center (0, 0),radius

A)
B)
C)
D)

Question 23

Determine the distance between the pair of points.
(0, 0) and (-10, -2)

A) 104
B)
C)
D) -12

Question 24

Graph the equation.

A)
B)

Question 25

Write the equation of the circle with the given center and radius.
Center (0, 0),radius 9

A)
B)
C)
D)

Question 26

Write the equation of the circle. Assume the radius is a whole number.

A) 4
B)
C)
D)

Question 27

Write the equation of the circle with the given center and radius.
Center (0, 1), radius

A)
B)
C)
D)

Question 28

Determine the midpoint of the line segment between the pair of points.

A)
B)
C)
D)

Question 29

Write the equation of the circle with the given center and radius.
Center (-8, -3), radius 1

A)
B)
C)
D)

Question 30

Determine the distance between the pair of points.
(-3, 3) and (-7, 0)

A) 25
B) 5
C) 10
D) 6

Question 31

Write the equation of the circle. Assume the radius is a whole number.

A)
B)
C)
D)

Question 32

Determine the midpoint of the line segment between the pair of points.
(0, 4) and (9, 8)

A) (-9, -4)
B)
C) (9, 12)
D)

Question 33

Write the equation of the circle with the given center and radius.
Center (0, -9), radius 8

A)
B)
C)
D)

Question 34

Determine the distance between the pair of points.
(4, 6) and (-4, -7)

A) -5
B)
C) 104
D)

Question 35

Write the equation of the circle with the given center and radius.
Center (-10, 10), radius

A)
B)
C)
D)

Question 36

Determine the distance between the pair of points.
(-2, -1) and (1, -7)

A) 9
B)
C)
D) 27

Question 37

Write the equation of the circle. Assume the radius is a whole number.

A)
B)
C)
D)

Question 38

Determine the distance between the pair of points.
(7, -1) and (3, -3)

A)
B)
C) 12
D) 2

Question 39

Determine the distance between the pair of points.
(6, 1) and (3, -5)

A) 27
B)
C) 3
D)

Question 40

Determine the distance between the pair of points.
(

A) 81
B) 8
C) 9
D)

Question 41

Graph the equation.

A)
B)
C)
D)

Question 42

Graph the equation.

A)
B)
C)
D)

Question 43

Graph the equation.

A)
B)
C)
D)

Question 44

Find the equation of the ellipse satisfying the given conditions.
(0, 6), (0, -6), (3, 0), (-3, 0) are the endpoints of the major and minor axes.

A)
B)
C)
D)

Question 45

Graph the equation.

A)
B)
C)
D)

Question 46

Graph the equation.

A)
B)
C)
D)

Question 47

Graph the equation.

A)
B)
C)
D)

Question 48

Graph the equation.

A)
B)
C)
D)

Question 49

Graph the equation.

A)
B)
C)
D)

Question 50

Graph the equation.

A)
B)
C)
D)

Question 51

Graph the equation.

A)
B)
C)
D)

Question 52

Graph the equation.

A)
B)
C)
D)

Question 53

Graph the equation.

A)
B)
C)
D)

Question 54

Use the method of completing the square to write the equation in standard form. Then graph the equation.

A)
B)
C)
D)

Question 55

Graph the equation.
(

A)
B)
C)
D)

Question 56

Graph the equation.

A)
B)
C)
D)

Question 57

Find the equation of the ellipse satisfying the given conditions.
(6, 0), (-6, 0), (0, 5), (0, -5) are the endpoints of the major and minor axes.

A)
B)
C)
D)

Question 58

Use the method of completing the square to write the equation in standard form. Then graph the equation.

A)
B)
C)
D)

Question 59

Graph the equation.

A)
B)
C)
D)

Question 60

Graph the equation.

A)
B)
C)
D)

Question 61

Write the equation in standard form (if necessary) and determine the equations of the asymptotes. Then graph the
equation.

A)
B)
C)
D)

Question 62

Solve the problem.
Find the equation of the ellipse, if (-8, -3) and (4, -3) are the endpoints of the major axis and (-2, -7) and (-2, 1) are the endpoints of the minor axis.

A)
B)
C)
D)

Question 63

Graph the equation.

A)
B)
C)
D)

Question 64

Solve the problem.
An arch for a bridge over a highway is in the form of a semi-ellipse. The top of the arch is 35 feet above ground. What should the span of the bridge be, rounded to the nearest hundredth of a foot, if the height 32 feet from the
Center is to be 16 feet above ground?

A) 71.96 ft
B) 140 ft
C) 79 ft
D) 35.98 ft

Question 65

Solve the problem.
The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 34 feet and the height of the arch over the center of the roadway is 9 feet. Two trucks plan to use this
Road. They are both 12 feet wide. Truck 1 has an overall height of 8 feet and Truck 2 has an overall height of
7 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.

A) Truck 1 can pass under the bridge, but Truck 2 cannot.
B) Neither Truck 1 nor Truck 2 can pass under the bridge.
C) Truck 2 can pass under the bridge, but Truck 1 cannot.
D) Both Truck 1 and Truck 2 can pass under the bridge.

Question 66

Solve the problem.
The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 32 feet and the height of the arch over the center of the roadway is 12 feet. Two trucks plan to use
This road. They are both 8 feet wide. Truck 1 has an overall height of 12 feet and Truck 2 has an overall height of
11 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.

A) Truck 2 can pass under the bridge, but Truck 1 cannot.
B) Neither Truck 1 nor Truck 2 can pass under the bridge.
C) Truck 1 can pass under the bridge, but Truck 2 cannot.
D) Both Truck 1 and Truck 2 can pass under the bridge.

Question 67

Indicate whether the equation represents an ellipse, hyperbola, circle, or parabola. In equations that contain both and terms, divide both sides of the equation by the constant term to put the equation in a more recognizable form.

A) Circle
B) Ellipse
C) Parabola
D) Hyperbola

Question 68

Indicate whether the equation represents an ellipse, hyperbola, circle, or parabola. In equations that contain both and terms, divide both sides of the equation by the constant term to put the equation in a more recognizable form.

A) Parabola
B) Hyperbola
C) Circle
D) Ellipse

Question 69

Write the equation in standard form (if necessary) and determine the equations of the asymptotes. Then graph the
equation.

A)
B)
C)
D)

Question 70

Write the equation in standard form (if necessary) and determine the equations of the asymptotes. Then graph the
equation.

A)
B)
C)
D)

Question 71

Write the equation in standard form (if necessary) and determine the equations of the asymptotes. Then graph the
equation.

A)
B)
C)
D)

Question 72

Indicate whether the equation represents an ellipse, hyperbola, circle, or parabola. In equations that contain both and terms, divide both sides of the equation by the constant term to put the equation in a more recognizable form.

A) Ellipse
B) Circle
C) Hyperbola
D) Parabola

Question 73

Solve the problem.
The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 32 feet and the height of the arch over the center of the roadway is 13 feet. Two trucks plan to use
This road. They are both 8 feet wide. Truck 1 has an overall height of 12 feet and Truck 2 has an overall height of
13 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.

A) Truck 1 can pass under the bridge, but Truck 2 cannot.
B) Both Truck 1 and Truck 2 can pass under the bridge.
C) Truck 2 can pass under the bridge, but Truck 1 cannot.
D) Neither Truck 1 nor Truck 2 can pass under the bridge.

Question 74

Determine the equations of the asymptotes for the equation.

A)
B)
C)
D)

Question 75

Write the equation in standard form (if necessary) and determine the equations of the asymptotes. Then graph the
equation.

A)
B)
C)
D)

Question 76

Solve the problem.
Find the equation of the hyperbola whose vertices are (0, 10) and (0, -10) and whose asymptotes are and

A)
B)
C)
D)

Question 77

Solve the problem.
A bridge is built in the shape of a semi-elliptical arch. It has a span of 96 feet. The height of the arch 29 feet from the center is to be 6 feet. Find the height of the arch at its center rounded to the nearest hundredth of a foot.

A) 9.93 ft
B) 6.29 ft
C) 7.53 ft
D) 29.23 ft

Question 78

Write the equation in standard form (if necessary) and determine the equations of the asymptotes. Then graph the
equation.

A)
B)
C)
D)

Question 79

Indicate whether the equation represents an ellipse, hyperbola, circle, or parabola. In equations that contain both and terms, divide both sides of the equation by the constant term to put the equation in a more recognizable form.

A) Hyperbola
B) Ellipse
C) Parabola
D) Circle

Question 80

Determine the equations of the asymptotes for the equation.
y

A)
B)
C)
D)