Quiz 8: Analytic Geometry in Two and Three Dimensions
Mathematics
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Q 105Q 105
Find the vertices and foci of the conic section without axis rotation by analyzing the graph geometrically in the xyplane.

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Q 106Q 106
Find the vertices and foci of the conic section without axis rotation by analyzing the graph geometrically in the xyplane.

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Q 107Q 107
Use the given substitutions to convert the equation to a (u, v) equation with no crossproduct term.

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Q 108Q 108
Use the given substitutions to convert the equation to a (u, v) equation with no crossproduct term.

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Q 109Q 109
Find the linear equations that can be used to convert an (x, y) equation to a (u, v) equation using the given angle of
rotation

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Q 110Q 110
Find the linear equations that can be used to convert an (x, y) equation to a (u, v) equation using the given angle of
rotation

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Q 111Q 111
A quadratic equation has been transformed using the rotation equations
Convert the
given point from (u, v) coordinates back to (x, y) coordinates.

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Q 112Q 112
A quadratic equation has been transformed using the rotation equations
Convert the
given point from (u, v) coordinates back to (x, y) coordinates.
parabola focus (1, 9)
A) (8, 4.8)
B) (6.6, 6.2)
C) (4.6, 7.8)
D) (6.2, 6.6)
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Q 113Q 113
Determine the appropriate rotation formulas to use so that the new equation contains no xyterm.

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Q 114Q 114
Determine the appropriate rotation formulas to use so that the new equation contains no xyterm.

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Q 115Q 115
Use axis of rotation formulas for x and y to transform the quadratic equation to an equation in (u, v) coordinates with no
crossproduct term.

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Q 116Q 116
Use axis of rotation formulas for x and y to transform the quadratic equation to an equation in (u, v) coordinates with no
crossproduct term.

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Q 117Q 117
Use axis of rotation formulas for x and y to transform the quadratic equation to an equation in (u, v) coordinates with no
crossproduct term.

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Q 118Q 118
Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.

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Q 119Q 119
Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.

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Q 120Q 120
Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.

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Q 121Q 121
Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.

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Q 122Q 122
Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.

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Q 123Q 123
Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.

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Q 124Q 124
Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.

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Q 125Q 125
Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.

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Q 126Q 126
Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.

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Q 127Q 127
Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.

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Q 128Q 128
Find the polar equation of the conic with focus at the pole, having the given properties. Identify the conic.

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Q 129Q 129
Find the polar equation of the conic with focus at the pole, having the given properties. Identify the conic.

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Q 130Q 130
Find the polar equation of the conic with focus at the pole, having the given properties. Identify the conic.

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Q 156Q 156
Write an equation for the sphere with the given point as its center and the given number as its radius.

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Q 157Q 157
Write an equation for the sphere with the given point as its center and the given number as its radius.

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