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Quadric Surfaces
Equations for Quadric Surfaces in 3D
6
Mathematics
Undergraduate 1
02/28/2011
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Term
Ellipsoid (egg)
 Definition
x^2 + y^2 + z^2
--- --- --- = 1
a^2 b^2 c^2
Term
Elliptic Paraboloid (bowl)
 Definition
x^2 + y^2 z
--- --- = ---
a^2 b^2 c
Term
Hyperbolic Paraboloid (saddle)
 Definition
x^2 y^2 z
--- - --- = ---
a^2 b^2 c
Term
Cone (hourglass)
 Definition
x^2 + y^2 z^2
--- --- = ---
a^2 b^2 c^2
Term
Hyperboloid of One Sheet (cooling tower)
 Definition
x^2 + y^2 - z^2
--- --- --- = 1
a^2 b^2 c^2
Term
Hyperboloid of Two Sheets (contact case reflected)
 Definition
-x^2 - y^2 + z^2
--- --- --- = 1
a^2 b^2 c^2
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