AnswersCollege Prep Math B - IC26Conic Sections: Parabolas

Conic Sections: Parabolas — Test Answers

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What is the radius of the circle with equation ?

Question illustration
A
unit
Option A
B
units
Option B
C
unit
Option C
D
units
Option D
2
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Gabe is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by a parabola that opens upward with a diameter of 4 in. and a depth of 1 in. The vertex of the parabola is at the origin. Where should Gabe place the bulb to ensure a perfect beam of light?

A
(0, 1)
B
(0, 4)
C
(1, 0)
D
(4, 0)
3

Graph .

Question illustration
A
On a coordinate plane, an Ellipse has center point (0, negative 1) and goes through points (0, 1), (7, negative 1), (0, negative 3), and (negative 7, negative 1).
Option A
B
On a coordinate plane, an Ellipse has center point (0, 1) and goes through points (0, 3), (7, 1), (0, negative 1), and (negative 7, 1).
Option B
C
On a coordinate plane, an ellipse has center point (0, 0) and goes through (0, 8), (2, 0), (0, negative 8), and (negative 2, 0).
Option C
D
On a coordinate plane, an ellipse has center point (0, 0.5) and goes through (0, 8), (2, 0), (0, negative 9), and (negative 2, 0).
Option D
4

A parabola has the following properties.Vertex at (–2, 1)Directrix is x = 5Which equation represents this parabola?

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

Convert the equation –9x2 + 25y2 – 100y – 125 = 0 into standard form.

A
StartFraction (y + 2) squared Over 9 EndFraction minus StartFraction x squared Over 25 EndFraction = 1
Option A
B
StartFraction (y minus 2) squared Over 5 EndFraction minus StartFraction 9 x squared Over 125 EndFraction = 1
Option B
C
StartFraction (y minus 2) squared Over 9 EndFraction minus StartFraction x squared Over 25 EndFraction = 1
Option C
D
StartFraction (y + 2) squared Over 5 EndFraction minus StartFraction 9 x squared Over 125 EndFraction = 1
Option D
6

A pair of listening posts picks up a sound, with one listening post recording the sound after the other. The equation represents possible locations of the sound source with units in feet. How far apart are the listening posts?

Question illustration
A
1,375 ft
B
2,750 ft
C
3,000 ft
D
6,000 ft
7

Aramis is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satellite can be modeled by , where x and y are modeled in inches. He realizes that the static is a result of the feed antenna shifting slightly off the focus point. Where should the feed antenna be placed?

Question illustration
A
0.75 in. below the vertex
B
0.75 in. to the right of the vertex
C
0.75 in. to the left of the vertex
D
0.75 in. above the vertex
8

The cable for a certain suspension bridge is modeled by a parabola with vertex (0, 0) at the center of the bridge. At a point that is 150 ft from the center of the bridge, the height of the cable is 30 ft. Which equation represents the height of the cable at a distance x feet from the center?

A
y = StartFraction 1 Over 3,000 EndFraction x squared
Option A
B
y = StartFraction 1 Over 750 EndFraction x squared
Option B
C
y = StartFraction 1 Over 25 EndFraction x squared
Option C
D
y = StartFraction 1 Over 6 EndFraction x squared
Option D
9

Which graph is represented by the equation (x + 3)2 + (y – 4)2 = 9?

A
On a coordinate plane, a circle has center (negative 3, 4) and radius 3.
Option A
B
On a coordinate plane, a circle has center (3, negative 4) and radius 9.
Option B
C
On a coordinate plane, a circle has center (3, negative 4) and radius 3.
Option C
D
On a coordinate plane, a circle has center (negative 3, 4) and radius 9.
Option D
10

A graphic designer creates a logo in the shape of an ellipse. The equation , with units in centimeters, represents the outer edge of the logo. How tall is the logo?

Question illustration
A
3.8 cm
B
7.6 cm
C
8 cm
D
16 cm
11

A plane intersecting a double-napped cone is parallel to the generator. Which conic section is formed?

A
circle
B
ellipse
C
hyperbola
D
parabola
12

Convert –2y2 + x – 4y + 6 = 0 into standard form.

A
x = 2(y + 1)2 – 6
B
x = 2(y + 1)2 – 8
C
x = 2(y + 1)2 – 7
D
x = 2(y + 1)2 + 8
13

The equation (x + 11)2 + (y – 27)2 = 2.25, with units in yards, represents a circular fountain in a park. The park entrance maps to (0, 0). If the positive x-axis represents east and the positive y-axis represents north, what is the location of the fountain relative to the park entrance?

A
11 yards east and 27 yards north
B
11 yards west and 27 yards north
C
11 yards east and 27 yards south
D
11 yards west and 27 yards south
14

Which equation represents a hyperbola?

A
4x2 + 3x + 4y2+ 5 = 0
B
2x2 – 5xy + 4y2 + 10x – y + 12 = 0
C
3x2 – 6xy + 3y2 + 5x – 2y + 1 = 0
D
3x2 + xy – 9y2 + 2x + 5 = 0
15

Fabio 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 is the focus of the flashlight?

Question illustration
A
(–2, –0.5)
B
(2, –5.5)
C
(2, 5.5)
D
(5.5, 2)
16

Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
17

Which conic section is represented by the following equation?9x2 – 5x – 3y2 – 2y + 4 = 0

A
circle
B
ellipse
C
parabola
D
hyperbola
18

Which graph represents the equation y = – (x – 1)2 + 1?

A
On a coordinate plane, a parabola opens up. It goes through (0, 2), has a vertex at (1, 1), and goes through (2, 2).
Option A
B
On a coordinate plane, a parabola opens down. It goes through (0, 0), has a vertex at (1, 1), and goes through (2, 0).
Option B
C
On a coordinate plane, a parabola opens down. It goes through (negative 2, 0), has a vertex at (negative 1, 1), and goes through (0, 0).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 2, 2), has a vertex at (negative 1, 1), and goes through (0, 2).
Option D
19

Which is the standard form of the equation of a parabola with a focus of (0, –3) and its vertex at the origin?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
20

Which graph represents 3x2 + 3y2 – 48x + 60y + 384 = 0?

A
On a coordinate plane, a circle has center (8, negative 10) and radius 6.
Option A
B
On a coordinate plane, a circle has center (negative 8, 10) and radius 6.
Option B
C
On a coordinate plane, a circle has center (negative 8, 10) and radius 11.
Option C
D
On a coordinate plane, a circle has center (8, negative 10) and radius 11.
Option D

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