The General Equation of Conic Sections Answers
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1
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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).
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).
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).
D
Option
2
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Which equation represents a parabola?
A
4x2 – 2x + 3y2 – y + 1 = 0B
x2 + x – 2y2 – 4y + 2 = 0C
–3x + 4y2 – 2y + 6 = 0D
2x2 + y2 – 4y + 6 = 03
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
B
StartFraction (x + 3) squared Over 9 EndFraction + StartFraction (y minus 2) squared Over 4 EndFraction = 0
C
StartFraction (x + 3) squared Over 4 EndFraction + StartFraction (y minus 2) squared Over 9 EndFraction = 1
D
StartFraction (x + 3) squared Over 4 EndFraction + StartFraction (y minus 2) squared Over 9 EndFraction = 0
4
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 + 39D
(y + 9)2 = 12x + 395
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).
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).
C
Option
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).
6
Graph x + 4 = –8(y – 2)2.
A
On a coordinate plane, a parabola opens to the right. It goes through (4, 3), has a vertex at (negative 4, 2), and goes through (4, 1).
B
On a coordinate plane, a parabola opens to the left. It goes through (negative 6, 1.5), has a vertex at (negative 4, 2), and goes through (negative 6, 2.5).
C
On a coordinate plane, a parabola opens to the right. It goes through (6, negative 1.5), has a vertex at (4, negative 2), and goes through (6, negative 2.5).
D
On a coordinate plane, a parabola opens to the left. It goes through (negative 4, negative 1), has a vertex at (4, negative 2), and goes through (4, negative 3).
7
Which conic section is represented by the following equation?3x2 – 7x + 8y2 – 2y + 1 = 0
A
circleB
ellipseC
parabolaD
hyperbola8
Which equation represents an ellipse?
A
2x2 – 4xy + 2y2 + x – 3y + 5 = 0B
2x2 – 6xy + y2 + 8x – y + 2 = 0C
3x2 + 7xy + 8y2 + 3x – 9y + 5 = 0D
9x2 + 3x + 9y2 – 2y + 5 = 09
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 4D
Mariah factored incorrectly in step 5. She should have factored to (x – 8)2 and (y + 4)2.10
Which conic section is represented by the following equation?9x2 – 5x – 3y2 – 2y + 4 = 0
A
circleB
ellipseC
parabolaD
hyperbolaDid you find these answers helpful?
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