AnswersPrecalculusThe General Equation of Conic Sections

Applications of Conics Answers

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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
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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
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

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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Applications of Conics Answers — Precalculus