QUADRIC FUNCTIONS (CALC III/MATH 241 UIUC)

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Calculus

Parametric Equations & polar Coordinates

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8 Terms

1
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ELLIPTIC PARABOLOID
z/c = x^2/a^2 + y^2/b^2
z/c = x^2/a^2 + y^2/b^2
2
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HYPERBOLIC PARABOLOID
z/c = x^2/a^2 - y^2/b^2
z/c = y^2/b^2 - x^2/a^2
z/c = x^2/a^2 - y^2/b^2 z/c = y^2/b^2 - x^2/a^2
3
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ELLIPSOID
x^2/a^2 + y^2/b^2 + z^2/c^2 = 1
x^2/a^2 + y^2/b^2 + z^2/c^2 = 1
4
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DOUBLE CONE
z^2 = x^2 + y^2
z^2 = x^2 + y^2
5
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HYPERBOLOID OF ONE SHEET
x^2/a^2 + y^2/b^2 - z^2/c^2 = 1
x^2/a^2 + y^2/b^2 - z^2/c^2 = 1
6
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HYPERBOLOID OF TWO SHEETS
-x^2/a^2 - y^2/b^2 + z^2/c^2 = 1
-x^2/a^2 - y^2/b^2 + z^2/c^2 = 1
7
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HYPERBOLA (HORIZONTAL TRANSVERSE)
x^2 - y^2 = 1
x^2 - y^2 = 1
8
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HYPERBOLA (VERTICAL TRANSVERSE)
y^2 - x^2 = 1
y^2 - x^2 = 1