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Quadratic Surfaces

Quadratic Surfaces. Calculus III – Thomas Chapter 12 Section 6. Quadratic Surfaces – General Form: Ax 2 + By 2 + Cz 2 + Dxy + Eyz +Fxz + Gx + Hy + Jz + K = 0 . R. M. E. Revised 2-25-07. Parabolic Cylinder y = x 2. Eliptical Cylinder x 2 + 4z 2 = 4. Hyperbolic Cylinder

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Quadratic Surfaces

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  1. Quadratic Surfaces Calculus III – Thomas Chapter 12 Section 6 Quadratic Surfaces – General Form: Ax2 + By2 + Cz2 + Dxy + Eyz +Fxz + Gx + Hy + Jz + K = 0 R. M. E. Revised 2-25-07 Parabolic Cylinder y = x2 Eliptical Cylinder x2 + 4z2 = 4 Hyperbolic Cylinder y2 –z2 = 1 Ellipsoid Elliptical Paraboloid x2+y2+z2= 1 a2 b2 c2 x2+y2= 1 a2 b2 Elliptical Cone Hyperboloids Hyperbolic Paraboloid(with saddle point x2+y2=z2a2 b2 c2 y2–x2=z b2 a2 c Hyperboliod of one sheet x2+y2–z2= 1 a2 b2 c2 asymptotic to eliptical cone Hyperboliod of two sheets z2–x2–y2= 1 c2 a2 b2

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