The General Equation of Conic Sections Answers
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1
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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)2.2
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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
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).
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).
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.
B
On a coordinate plane, a circle has center (negative 8, 10) and radius 6.
C
On a coordinate plane, a circle has center (negative 8, 10) and radius 11.
D
On a coordinate plane, a circle has center (8, negative 10) and radius 11.
5
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
B
Option
C
Option
D
Option
6
Which conic section is represented by the following equation?9x2 – 5x – 3y2 – 2y + 4 = 0
A
circleB
ellipseC
parabolaD
hyperbola7
Which conic section is represented by the following equation?3x2 – 7x + 8y2 – 2y + 1 = 0
A
circleB
ellipseC
parabolaD
hyperbola8
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).
9
Graph .
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).
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).
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).
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).
10
Graph .
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).
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).
C
On a coordinate plane, an Ellipse has center (4, 0) and goes through (6, 0), (4, negative 3), (2, 0) and (4, 3).
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).
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