AnswersCollege Prep Math B - IC26Conic Sections: Parabolas

Conic Sections: Parabolas — Test Answers

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Yeric designs a circular cushion by cutting pieces of fabric to sew together as the front and back of the cushion. He cuts each piece of fabric according to the equation x2 + y2 = 100 with units in inches. Based on this equation, what is the diameter of the cushion?

A
5 in.
B
10 in.
C
20 in.
D
100 in.
2
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A pair of listening posts is 4,000 ft apart. They both pick up a sound, but one listening post records the sound 1.5 seconds after the other listening post. The sound is d1 feet from the first listening post and d2 feet from the second listening post. Assume sound travels at 1,100 ft/s. Which equation of a hyperbola can be used to determine possible locations of the origin of the sound?Note that

Question illustration
A
StartFraction x squared Over 825 EndFraction minus StartFraction y squared Over 1,175 EndFraction = 1
Option A
B
StartFraction x squared Over 680,625 EndFraction minus StartFraction y squared Over 3,319,375 EndFraction = 1
Option B
C
StartFraction x squared Over 680,625 EndFraction minus StartFraction y squared Over 4,000,000 EndFraction = 1
Option C
D
StartFraction x squared Over 2,722,500 EndFraction minus StartFraction y squared Over 13,277,500 EndFraction = 1
Option D
3

What is the diameter of a circle with the equation (x – 4)2 + (y + 6)2 = 64?

A
4
B
8
C
16
D
64
4

Review the graph of circle A.

Question illustration
A
(x – 1)2 + (y – 1)2 = 5
B
(x + 1)2 + (y + 1)2 = 5
C
(x – 1)2 + (y – 1)2 = 25
D
(x + 1)2 + (y + 1)2 = 25
5

Which graph represents 9x2 – 16y2 – 54x + 64y – 127 = 0?

A
On a coordinate plane, an Ellipse has center (3, 2) and goes through (7, 2), (3, negative 1), (negative 1, 2), and (3, 5).
Option A
B
On a coordinate plane, an Ellipse has center (3, 2) and goes through (6, 2), (3, negative 2), (0, 3), and (3, 6).
Option B
C
Option
Option C
D
On a coordinate plane, one part of a conic graph goes through (negative 1, 6), has a vertex at (0, 2), and goes through (negative 1, negative 1). The second part goes through (7, 6), has a vertex at (6, 2), and goes through (7, negative 1).
Option D
6

A picture frame has the shape of an ellipse defined by the equation with units in inches. A hook is placed on the back of the picture frame to hang it on the wall. The hook is located at one of the foci of the ellipse. What is the distance from the hook to the top of the picture frame?

Question illustration
A
2 in.
B
4 in.
C
6 in.
D
8 in.
7

Which is the standard form of the equation of the parabola that has a vertex of (–4, –3) and a directrix of x = 2?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

Which conic section is represented by the following equation?–5x2 + 9xy + 5y2 + 6x – 4y + 11 = 0

A
circle
B
ellipse
C
parabola
D
hyperbola
9

Rene is designing a satellite that is the shape of a parabola that opens upward with a diameter of 8 in. and a depth of 2 in. The feed antenna focuses the incoming radio waves. At what point should the feed antenna be placed?

A
(–8, 0)
B
(–2, 0)
C
(0, 2)
D
(0, 8)
10

Which conic section is represented by the following equation?–5x2 + 10xy – 5y2 + 2x – y + 4 = 0

A
circle
B
ellipse
C
parabola
D
hyperbola
11

Which equation represents a parabola with its vertex at (1, –5) and its focus at (1, 0)?

A
= (x – 1)2
Option A
B
20(y + 5) = (x – 1)2
C
–20(y + 5) = (x – 1)2
D
= (x – 1)2
Option D
12

Convert 9x2 + 4y2 – 54x – 8y – 59 = 0 into standard form.

A
StartFraction (x + 3) squared Over 4 EndFraction + StartFraction (y + 1) Over 9 EndFraction = 1
Option A
B
StartFraction (x minus 3) squared Over 4 EndFraction + StartFraction (y minus 1) Over 9 EndFraction = 1
Option B
C
StartFraction (x + 3) squared Over 16 EndFraction + StartFraction (y + 1) Over 36 EndFraction = 1
Option C
D
StartFraction (x minus 3) squared Over 16 EndFraction + StartFraction (y minus 1) Over 36 EndFraction = 1
Option D
13

Which image shows a plane slicing a double-napped cone to produce a hyperbola?

A
2 cones are stacked at their points. A horizontal plane goes through the center of a cone.
Option A
B
2 cones are stacked at their points. A plane goes diagonally through the center of a cone.
Option B
C
2 cones are stacked at their points. A plane goes diagonally along the sides of the cones.
Option C
D
2 cones are stacked at their points. A plane goes diagonally through both cones.
Option D
14

A mirror has a parabolic surface defined by the equation y = x2 with the vertex (0, 0) at the center of the mirror. When the width of the mirror is 8 inches, what is the depth, y, of the mirror?

Question illustration
A
in.
Option A
B
in.
Option B
C
in.
Option C
D
in.
Option D
15

Gabriella is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by where x and y are measured in inches. Where should she place the bulb to ensure a perfect beam of light?

Question illustration
A
6.5 in. to the left of the vertex
B
6.5 in. above the vertex
C
6.5 in. to the right of the vertex
D
6.5 in. below the vertex

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