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A general second degree equation to three variables ax^2 + by^2+ cz^2 + 2fyz + 2gzx + 2hxy + 2ux + 2vy + 2wz + d=0 represents a conicoid
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The standard equation of central conicoid with centre (0,0,0) is Ax2+By2+Cz2=1 various kind of central conicoid are as follows. 1) ellipsoid 2)hyperboloid of one sheet 3) hyperboloid of two sheets 4) virtual ellipsoid