AnswersPrecalculusThe General Equation of Conic Sections

The General Equation of Conic Sections Answers

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Which conic section is represented by the following equation?5x2 – x + 5y2 – 3y – 12 = 0

A
circle
B
ellipse
C
parabola
D
hyperbola
2
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Which equation represents a parabola?

A
4x2 – 2x + 3y2 – y + 1 = 0
B
x2 + x – 2y2 – 4y + 2 = 0
C
–3x + 4y2 – 2y + 6 = 0
D
2x2 + y2 – 4y + 6 = 0
3

Convert the equation into standard form.25x2 – 9y2 + 200x + 18y + 166 = 0

A
StartFraction (x minus 8) squared Over 9 EndFraction minus StartFraction (y + 2) squared Over 25 EndFraction = 1
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
4

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
5

Which equation represents an ellipse?

A
2x2 – 4xy + 2y2 + x – 3y + 5 = 0
B
2x2 – 6xy + y2 + 8x – y + 2 = 0
C
3x2 + 7xy + 8y2 + 3x – 9y + 5 = 0
D
9x2 + 3x + 9y2 – 2y + 5 = 0
6

What is the standard form of the following equation?4x2 + 9y2 + 24x – 36y + 36 = 0

A
StartFraction (x + 3) squared Over 9 EndFraction + StartFraction (y minus 2) squared Over 4 EndFraction = 1
Option A
B
StartFraction (x + 3) squared Over 9 EndFraction + StartFraction (y minus 2) squared Over 4 EndFraction = 0
Option B
C
StartFraction (x + 3) squared Over 4 EndFraction + StartFraction (y minus 2) squared Over 9 EndFraction = 1
Option C
D
StartFraction (x + 3) squared Over 4 EndFraction + StartFraction (y minus 2) squared Over 9 EndFraction = 0
Option D
7

Which graph represents 49x2 + 4y2 + 196x – 40y + 100 = 0?

A
On a coordinate plane, one part of a conic graph goes through (negative 1, 1), has a vertex at (0, negative 5), and goes through (negative 1, negative 12). The second part goes through (5, 1), has a vertex at (4, negative 6), and goes through (5, negative 12).
Option A
B
On a coordinate plane, one part of a conic graph goes through (negative 5, 12), has a vertex at (negative 4, 5), and goes through (negative 5, negative 2). The second part goes through (1, 12), has a vertex at (0, 5), and goes through (1, negative 2).
Option B
C
On a coordinate plane, an Ellipse has center (2, negative 5) and goes through (4, negative 5), (2, negative 12), (0, negative 5), and (2, 2).
Option C
D
Option
Option D
8

Mariah converted the following equation into standard form.25x2 + 25y2 – 200x + 100y + 4 = 025x2 – 200x + 25y2 + 100y = –425(x2 – 8x) + 25(y2 + 4y) = –425(x2 – 8x + 16) + 25(y2 + 4y + 4) = –4 + 16 + 425(x – 4)2 + 25(y + 2)2 = 16

A
Mariah did not make an error.
B
Mariah listed the center incorrectly. The center should be (–4, 2).
C
Mariah should have added 400 and 100 to the right side of the equation in step 4
D
Mariah factored incorrectly in step 5. She should have factored to (x – 8)2 and (y + 4)2.
9

Which conic section is represented by the following equation?3x2 – 7x + 8y2 – 2y + 1 = 0

A
circle
B
ellipse
C
parabola
D
hyperbola
10

Which graph represents 25x2 – 4y2 – 72y – 424 = 0?

A
On a coordinate plane, an Ellipse has center (0, negative 9) and goes through (0, negative 4), (2, negative 9), (0, negative 14), (negative 2, negative 9).
Option A
B
On a coordinate plane, an Ellipse has center (0, negative 9) and goes through (0, negative 7), (5, negative 9), (0, negative 11), and (negative 5, negative 9).
Option B
C
Option
Option C
D
On a coordinate plane, one part of a conic graph goes through (negative 7, negative 7), has a vertex at (negative 5, negative 9), and goes through (negative 7, negative 12). The second part goes through (7, negative 7), has a vertex at (5, negative 9), and goes through (7, negative 12).
Option D

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