Which Quadric Is Which?

A quadric surface is the zero set of a quadratic expression in three variables—here, the 3D Cartesian coordinates , , and . There are precisely 17 types of quadrics, but some of them are degenerate and others are imaginary.
The nonparabolic family is given by
,
where , , and can be , , or .
The parabolic family (which overlaps the nonparabolic family somewhat) is given by
.
This Demonstration shows the chosen polynomial, identifies its type, and plots the zero set. The checkbox toggles between the nonparabolic and parabolic families. All 17 types are represented.

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