AnswersPrecalculusThe General Equation of Conic Sections

The General Equation of Conic Sections Answers

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Write the equation y2 + 6y – 12x – 39 = 0 in standard form.

A
(y + 9)2 = 12(x + 4)
B
(y + 3)2 = 12(x + 4)
C
(y + 3)2 = 12x + 39
D
(y + 9)2 = 12x + 39
3

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
4

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
5

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
7

Graph .

Question illustration
A
On a coordinate plane, one part of a conic graph goes through (negative 1, 1), has a vertex at (0, negative 3), and goes through (negative 1, negative 7).
Option A
B
On a coordinate plane, one part of a conic graph goes through (negative 11, 8), has a vertex at (negative 10, 3), and goes through (negative 11, negative 1). The other part goes through (1, 7) has a vertex at (0, 3), and goes through (1, negative 1).
Option B
C
On a coordinate plane, an Ellipse has center (5, negative 3) and goes through (10, negative 3), (5, negative 9), (0, negative 3), and (5, 3).
Option C
D
On a coordinate plane, an Ellipse has center (5, 3) and goes through (negative 5, 9), (0, 3), (5, negative 3), and (negative 10, 3).
Option D
9

Graph .

Question illustration
A
On a coordinate plane, an Ellipse has center point (4, 0) and goes through (4, 2), (7, 0), (4, negative 2), and (1, 0).
Option A
B
On a coordinate plane, an Ellipse has center point (negative 4, 0) and goes through (negative 1, 0), (negative 4, 2), (negative 7, 0) and (negative 4, negative 2).
Option B
C
On a coordinate plane, an Ellipse has center (4, 0) and goes through (6, 0), (4, negative 3), (2, 0) and (4, 3).
Option C
D
On a coordinate plane, an Ellipse has center (negative 4, 0) and goes through (negative 2, 0), (negative 4, 3), (negative 6, 0) and (negative 4, negative 3).
Option D
10

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

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