Answers25-26 KCS21 Precalculus ICApplications of Conics

Applications of Conics Answers

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1
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A mirror is the shape of an ellipse defined by with units in feet. Which statement identifies the orientation of the mirror and its greatest dimension?

Question illustration
A
The mirror has a vertical orientation and is 5.4 ft tall.
B
The mirror has a horizontal orientation and is 5.4 ft wide.
C
The mirror has a vertical orientation and is 7.29 ft tall.
D
The mirror has a horizontal orientation and is 7.29 ft wide.
2
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Ailani draws a map of her local town. She places the town hall at the origin of a coordinate plane and represents a lake with a circle drawn on the map. The center of the lake is 19 miles east and 3 miles south of the town hall, and the radius of the lake is 0.5 miles.If the positive x-axis represents east and the positive y-axis represents north, which equation represents the lake?

A
(x + 19)2 + (y – 3)2 = 0.5
B
(x – 19)2 + (y + 3)2 = 0.5
C
(x + 19)2 + (y – 3)2 = 0.25
D
(x – 19)2 + (y + 3)2 = 0.25
3

Lori tosses a ball into the air. The equation y = –16(x – 1)2 + 25 models the height, y, in feet, of the ball after x seconds. What is the maximum height the ball reaches?

A
1 ft
B
9 ft
C
16 ft
D
25 ft
4

A cooling tower is 120 meters tall. The sides of the tower are in the shape of a hyperbola defined by the equation with units in meters. The center of the tower is at the origin. How wide is the tower at the top?

Question illustration
A
50 m
B
92 m
C
100 m
D
184 m
5

The difference of the squares of two numbers is equal to 9. Let x represent the larger number and y represent the smaller number. Which graph shows all possible values of x and y?

A
On a coordinate plane, one part of a conic graph goes through (negative 6, 5), has a vertex at (negative 3, 0), and goes through (negative 6, negative 5). The second part goes through (6, 5), has a vertex at (3, 0), and goes through (6, negative 5).
Option A
B
On a coordinate plane, the first part of a conic graph goes through (negative 5, 6), has a vertex at (0, 3), and goes through (5, 6). The second part goes through (5, negative 6), has a vertex at (0, negative 3), and goes through (5, negative 6).
Option B
C
On a coordinate plane, a circle has center (0, 0) and radius 3.
Option C
D
On a coordinate plane, a circle has center (0, 0) and radius 9.
Option D
6

A pair of radar stations monitors the path of a helicopter. Station A is located at the origin of a coordinate plane. Station B is located 100 miles east of station A. The difference in the distances from the helicopter to each station is 60 miles. Which equation represents the possible locations of the helicopter?

A
StartFraction (x minus 50) squared Over 900 EndFraction minus StartFraction y squared Over 1,600 EndFraction = 1
Option A
B
StartFraction (x minus 50) squared Over 3,600 EndFraction minus StartFraction y squared Over 6,400 EndFraction = 1
Option B
C
StartFraction (x minus 100) squared Over 900 EndFraction minus StartFraction y squared Over 1,600 EndFraction = 1
Option C
D
StartFraction (x minus 100) squared Over 3,600 EndFraction minus StartFraction y squared Over 6,400 EndFraction = 1
Option D
7

A serving dish has a parabolic surface with the vertex (0, 0) at the center of the dish. When the width of the dish is 6 inches, the depth of the dish is 3 inches. The equation that models the shape of the serving dish is y = ax2. What is the value of a?

A
StartFraction 1 Over 12 EndFraction
Option A
B
One-third
Option B
C
One-half
Option C
D
1
8

A carpenter designs a tabletop in the shape of an ellipse 7 feet long and 4 feet wide. The carpenter sketches a drawing of the tabletop on a coordinate plane. The center of the tabletop is at the origin, the length falls along the x-axis, and the width falls along the y-axis. Which equation represents the tabletop?

A
StartFraction x squared Over 49 EndFraction + StartFraction y squared Over 16 EndFraction = 1
Option A
B
StartFraction y squared Over 49 EndFraction + StartFraction x squared Over 16 EndFraction = 1
Option B
C
StartFraction x squared Over 12.25 EndFraction + StartFraction y squared Over 4 EndFraction = 1
Option C
D
StartFraction y squared Over 12.25 EndFraction + StartFraction x squared Over 4 EndFraction = 1
Option D
9

A company produces circular drink coasters. The equation x2 + y2 = 18.0625, with units in inches, represents the size of a coaster. Each coaster is cut from a square piece of cardboard. What is the minimum possible area of each cardboard piece?

A
4.25 in2
B
8.5 in2
C
18.0625 in2
D
72.25 in2
10

Antonio constructs a model of a moon orbiting a planet along an elliptical orbit. The equation , with units in inches, represents the shape of the orbit. If the planet is located at one of the foci, which phrase describes a possible location of the model planet relative to the center?

Question illustration
A
approximately 0.5 in. below the center
B
approximately 4.3 in. above the center
C
approximately 0.5 in. to the left of the center
D
approximately 4.3 in. to the right of the center

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