Answers25-26 KCS21 Precalculus ICApplications of Conics

Applications of Conics Answers

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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?

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A
50 m
B
92 m
C
100 m
D
184 m
2
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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?

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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
3

The profile of a dam is modeled by the equation , where x represents horizontal distance and y represents height, both in meters. Review the diagram of the dam.

Question illustration
A
24 meters
B
36 meters
C
54 meters
D
72 meters
4

An architect designed a lobby wall to have an embedded circular clock. The equation (x – 4)2 + (y – 7)2 = 1, with units in meters, represents the location of the clock relative to the bottom left corner of the wall. How high above the ground is the center of the clock?

A
1 m
B
4 m
C
7 m
D
8 m
5

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
6

A drone has an effective range represented by a circle on a coordinate plane. The points (–12, 3) and (–6, –5) are endpoints of a diameter of this boundary. Which equation represents the effective range boundary for the drone?

A
(x + 9)2 + (y + 1)2 = 25
B
(x – 9)2 + (y – 1)2 = 25
C
(x + 9)2 + (y + 1)2 = 100
D
(x – 9)2 + (y – 1)2 = 100
7

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
8

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
9

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
10

A company is introducing a new product. The equation y = –0.001(x – 600)2 + 90 predicts the expected profit, in thousands of dollars, where x represents the number of thousands of units of the product sold by the company. How many units must be sold to yield a maximum profit?

A
90
B
600
C
90,000
D
600,000

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