Quadrics

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A surface defined by an algebraic equation of degree two is called a quadric. Spheres, circular cylinders, and circular cones are quadrics. By means of a rigid motion, any quadric can be transformed into a quadric having one of the following equations (where a,b,c0):

(1) Real ellipsoid x/a+y/b+z/c=1 (2) Imaginary ellipsoid x/a+y/b+z/c=-1 (3) Hyperboloid of one sheet x/a+y/b-z/c=1 (4) Hyperboloid of two sheets x/a+y/b-z/c=-1 (5) Real quadric cone x/a+y/b-z/c=0 (6) Imaginary quadric cone x/a+y/b+z/c=0 (7) Elliptic paraboloid x/a+y/b+2z=0 (8) Hyperbolic paraboloid x/a-y/b+2z=0 (9) Real elliptic cylinder x/a+y/b=1 (10) Imaginary elliptic cylinder x/a+y/b=-1 (11) Hyperbolic cylinder x/a-y/b=1 (12) Real intersecting planes x/a-y/b=0 (13) Imaginary intersecting planes x/a+y/b=0 (14) Parabolic cylinder x+2y=0 (15) Real parallel planes x=1 (16) Imaginary parallel planes x=-1 (17) Coincident planes x=0

- ref.1 - Quadrics - (http://www.geom.uiuc.edu/docs/reference/CRC-formulas/node61.html)

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