Deck 10: The Conic Sections

Question 1

Find the vertex of the parabola, and determine whether the parabola opens upward, downward, to the left, or to the right.

A) (3, 5), up
B) (-3, -5), up
C) (3, -5), down
D) (-3, 5), down

Answer 1

(-3, -5), up

Question 2

Using the graph of the parabola, determine the coordinates of the vertex and focus, and the equation of the directrix.

A) Vertex (1, 4), focus (1, 2), directrix y = 6
B) Vertex (1, 6), focus (1, 4), directrix y = 2
C) Vertex (1, 4), focus (1, 6), directrix y = 2
D) Vertex (1, 4), focus (1, 6), directrix x = 2

Answer 2

Vertex (1, 4), focus (1, 6), directrix y = 2

Question 3

Find the vertex of the parabola, and determine whether the parabola opens upward, downward, to the left, or to the right.

A) (-9, 4), down
B) (9, -16), up
C) (9, -4), up
D) (-4, 9), down

Answer 3

(-4, 9), down

Question 4

Find the equation of the parabola determined by the given information.
Vertex at (-3, -14), directrix y = -19

A)
B)
C)
D)

Question 5

Find the equation of the parabola determined by the given information.
Focus at (7, -7), directrix x = -1

A)
B)
C)
D)

Question 6

Find the equation of the parabola determined by the given information.
Vertex at the origin, focus at (8, 0)

A)
B)
C)
D)

Question 7

Find the vertex of the parabola, and determine whether the parabola opens upward, downward, to the left, or to the right.

A) (-4, 3), up
B) (4, -3), down
C) (4, -9), down
D) (-3, 4), up

Question 8

Find the equation of the parabola determined by the given information.
Vertex at (-7, -4), directrix x = -9

A)
B)
C)
D)

Question 9

Find the equation of the parabola determined by the given information.
Focus at (0, -2), directrix y = 2

A)
B)
C)
D)

Question 10

Find the equation of the parabola determined by the given information.
Focus at (2, 0), directrix x = -2

A)
B)
C)
D)

Question 11

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

A)
B)
C)
D)

Question 12

Find the equation of the parabola determined by the given information.
Vertex at the origin, focus at

A)
B)
C)
D)

Question 13

Using the graph of the parabola, determine the coordinates of the vertex and focus, and the equation of the directrix.

A) Vertex (-4, 2), focus (-5, 2), directrix x = -3
B) Vertex (-4, 2), focus (-3, 2), directrix x = -5
C) Vertex (-4, 2), focus (-5, 2), directrix y = -3
D) Vertex (-5, 2), focus (-4, 2), directrix x = -3

Question 14

Find the equation of the parabola determined by the given information.
Focus at (-3, -2), directrix y = -6

A)
B)
C)
D)

Question 15

Find the vertex of the parabola, and determine whether the parabola opens upward, downward, to the left, or to the right.

A) (3, 0), down
B) (-3, 3), up
C) (-3, -3), up
D) (0, 3), down

Question 16

Find the vertex of the parabola, and determine whether the parabola opens upward, downward, to the left, or to the right.

A) (6, 3), down
B) (6, -3), up
C) (-6, -3), down
D) (-6, 3), up

Question 17

Find the equation of the parabola determined by the given information.
Vertex at the origin, focus at (0, 10)

A)
B)
C)
D)

Question 18

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

A)
B)
C)
D)

Question 19

Find the vertex of the parabola, and determine whether the parabola opens upward, downward, to the left, or to the right.

A) (-2, 0), up
B) (0, -2), up
C) (2, 2), down
D) (2, -2), down

Question 20

Find the equation of the parabola determined by the given information.
Vertex at the origin, focus at

A)
B)
C)
D)

Question 21

Find the vertex of the parabola, and determine whether the parabola opens upward, downward, to the left, or to the right.

A) (5, -8), right
B) (-25, 8), left
C) (-5, 8), left
D) (8, -5), right

Question 22

Find the vertex, axis of symmetry, and y-intercept of the parabola that has the given focus and directrix.
Focus (-5, -6), directrix y = 2

A)
B) (-5, -2), y = -5, (0, -2)
C) (-2, -5), y = -2, (0, -5)
D)

Question 23

Find the focus and the directrix of the parabola.

A)
B) (0, 4); y = -8
C) (3, -4); x = 5
D) (5, 4); y = 3

Question 24

Find the vertex of the parabola, and determine whether the parabola opens upward, downward, to the left, or to the right.

A) (-2, -2), right
B) (2, 0), left
C) (0, 2), left
D) (2, -2), right

Question 25

Find the focus and the directrix of the parabola.

A) (-14, 5); x = -16
B) (2, 5); x = 8
C)
D)

Question 26

Find the coordinates of the vertex of the parabola.

A) (5, 1)
B) (1, 5)
C) (-1, -5)
D) (-5, -1)

Question 27

Find the focus and the directrix of the parabola.

A) (5, -2); y = 0
B) (5, 0); y = -2
C)
D) (5, -5); y = -3

Question 28

Find the vertex of the parabola, and determine whether the parabola opens upward, downward, to the left, or to the right.

A) (-3, 4), left
B) (9, -4), right
C) (4, -3), left
D) (4, -3), right

Question 29

Find the coordinates of the vertex of the parabola.

A) (0, -8)
B) (-8, -9)
C) (-9, 0)
D) (-9, -8)

Question 30

Find the coordinates of the vertex of the parabola.

A) (-5, -4)
B) (-4, -5)
C) (4, 5)
D) (5, 4)

Question 31

Find the vertex, axis of symmetry, and y-intercept of the parabola that has the given focus and directrix.

A)
B)
C)
D)

Question 32

Find the coordinates of the vertex of the parabola.

A) (-5, 4)
B) (5, -4)
C) (4, -5)
D) (-4, 5)

Question 33

Find the coordinates of the vertex of the parabola.

A) (1, 0)
B) (0, -1)
C) (0, 1)
D) (-1, 0)

Question 34

Find the coordinates of the vertex of the parabola.

A) (-1, -4)
B) (1, 4)
C) (-4, -1)
D) (4, 1)

Question 35

Find the coordinates of the vertex of the parabola.

A) (2, 4)
B) (2, 0)
C) (4, 0)
D) (4, 2)

Question 36

Find the coordinates of the vertex of the parabola.

A) (6, 3)
B) (6, 0)
C) (0, 3)
D) (3, 6)

Question 37

Find the coordinates of the vertex of the parabola.

A) (4, 3)
B) (0, 4)
C) (3, 4)
D) (3, 0)

Question 38

Find the vertex of the parabola, and determine whether the parabola opens upward, downward, to the left, or to the right.

A) (5, 5), left
B) (-5, 0), right
C) (0, -5), right
D) (-5, 5), left

Question 39

Find the coordinates of the vertex of the parabola.

A) (1, 7)
B) (7, 1)
C) (0, 7)
D) (1, 0)

Question 40

Find the focus and the directrix of the parabola.

A)
B) (5, 0); x = -4
C) (5, 6); x = 10
D)

Question 41

Solve.
A building has an entry with the shape of a parabolic arch 14 ft high and 22 ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

A)
B)
C)
D)

Question 42

Graph the parabola.

A)
B)
C)
D)

Question 43

Graph the parabola.

A)
B)
C)
D)

Question 44

Graph the parabola.

A)
B)
C)
D)

Question 45

Using the graph of the ellipse, determine the coordinates of the foci, vertices, and center.

A)
B)
C)
D)

Question 46

Graph the parabola.

A)
B)
C)
D)

Question 47

Solve.
A radio telescope has a parabolic surface. If it is 1 m deep and 20 m wide, how far is the focus from the vertex?

A) 25 m
B) 1 m
C) 100 m
D) 5 m

Question 48

Graph the parabola.

A)
B)
C)
D)

Question 49

Solve.
A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 10 m down from the top of the dome the ceiling is 16 m wide, find the best location for
The light source.

A) 1.6 m down from the top
B) 3.2 m down from the top
C) 6.4 m down from the top
D) 4.8 m down from the top

Question 50

Graph the parabola.

A)
B)
C)
D)

Question 51

Graph the parabola.

A)
B)
C)
D)

Question 52

Graph the parabola.

A)
B)
C)
D)

Question 53

Graph the parabola.

A)
B)
C)
D)

Question 54

Graph the parabola.

A)
B)
C)
D)

Question 55

Solve.
A cross-section of an irrigation canal is a parabola. If the surface of the water is 45 ft wide and the canal is 37 ft deep at the center, how deep is it 4 ft from the edge?

A) 12 ft
B) 30.7 ft
C) 6.3 ft
D) 25 ft

Question 56

Graph the parabola.

A)
B)
C)
D)

Question 57

Graph the parabola.

A)
B)
C)
D)

Question 58

Graph the parabola.

A)
B)
C)
D)

Question 59

Solve.
A tunnel is in the shape of a parabola. The maximum height is 17 m and it is 7 m wide at the base. What is the vertical clearance 2 m from the edge of the tunnel?
A = 17 m
B = 7 m

A) 1.7 m
B) 13.9 m
C) 3.1 m
D) 15.3 m

Question 60

Graph the parabola.

A)
B)
C)
D)

Question 61

Write an equation for the ellipse.
Foci and y-intercepts

A)
B)
C)
D)

Question 62

Write an equation for the ellipse.
Foci and y-intercepts

A)
B)
C)
D)

Question 63

Match the given graph with its equation.

A)
B)
C)
D)

Question 64

Write an equation for the ellipse.
Foci and x-intercepts

A)
B)
C)
D)

Question 65

Write an equation for the ellipse.

A)
B)
C)
D)

Question 66

Graph the ellipse.

A)
B)
C)
D)

Question 67

Match the given graph with its equation.

A)
B)
C)
D)

Question 68

Find the foci of the ellipse.

A) (4, -4), (4, 2)
B) (-4, 4), (2, 4)
C) (-5, 4), (3, 4)
D) (4, -5), (4, 3)

Question 69

Find the foci of the ellipse.

A) (-3, 0), (3, 0)
B) (-4, 0), (4, 0)
C) (0, -4), (0, 4)
D) (0, -3), (0, 3)

Question 70

Find the foci of the ellipse.

A) (-1, -7), (-1, 9)
B) (-1, -5), (-1, 7)
C) (-7, -1), (9, -1)
D) (-5, -1), (7, -1)

Question 71

Write an equation for the ellipse.
Foci and y-intercepts

A)
B)
C)
D)

Question 72

Write an equation for the ellipse.
Foci and x-intercepts

A)
B)
C)
D)

Question 73

Graph the ellipse.

A)
B)
C)
D)

Question 74

Write an equation for the ellipse.
Foci and y-intercepts

A)
B)
C)
D)

Question 75

Find the foci of the ellipse.

A) (-4, -13), (-4, 5)
B) (-16, -4), (8, -4)
C) (-13, -4), (5, -4)
D) (-4, -16), (-4, 8)

Question 76

Using the graph of the ellipse, determine the coordinates of the foci, vertices, and center.

A)
B)
C)
D) Foci (-5, -3) and (1, -3), vertices (-2, 1) and (-2, -7), center (-2, -3)

Question 77

Write an equation for the ellipse.
Foci and x-intercepts

A)
B)
C)
D)

Question 78

Find the foci of the ellipse.

A) (0, -12), (0, 12)
B) (-12, 0), (12, 0)
C) (0, -9), (0, 9)
D) (-9, 0), (9, 0)

Question 79

Graph the ellipse.

A)
B)
C)
D)

Question 80

Graph the ellipse.

A)
B)
C)
D)