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Elliptical Paraboloid
1 not squared, other 2 squared have same sign
Ellipsoid
all three squared, all positive, equals positive constant
Elliptical Cone
all squared, mixed signs, no constant term
Hyperboloid of 1 Sheet
all squared, two positive, one negative, positive constant
Hyperboloid of 2 Sheets
all squared, one positive, two negative, positive constant
Hyperbolic Paraboloid
two squared with different signs