Quadrics
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,c 0):
(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......
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Quadrics
Quadrics 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,
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