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(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
The five nondegenerate real quadrics
Figure 1: The ellipsoid (1)...
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(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
The five nondegenerate real quadrics
Figure 1: The ellipsoid (1)...
Essay fragment
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