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Quadratic Surfaces

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sogeyuse's version from 2017-10-01 21:05

Section

Question Answer
Any two variables (the third undefined)Cylinder
3 Positive Coefficients (x2+y2+z2 = 1)Ellipsoid
One Negative Coefficient = 1 (x2+y2-z2 = 1)Hyperboloid (1 Sheet - Open on opposite signed var)
Two Negative Coefficients = 1 (-x2-y2+z2 = 1)Hyperboloid (2 Sheets - Open on opposite signed var)
1 negative coefficient = 0, (x2+y2-z2 = 0)Cone
x2+y2=z, x/y have same signElliptic Paraboloid (Opens on linear term +=up, -=down)
x2-y2=z, x/y have opposite signHyperbolic Paraboloid (Think of PRINGLES)
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