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Squared terms: all 3, signs: all agree, right side: positive
ellipsoid (sphere if equal)
Squared terms: all 3, signs: one minus, right side: positive
Hyperboloid of one sheet
Squared terms: all 3, signs: two minus, right side: positive
Hyperboloid of two sheet
Squared terms: all 3, signs: mixed, right side: zero
elliptic cone
Squared terms: two, signs: the two agree, right side: ____
elliptic paraboloid
Squared terms: two, signs: the two diagree, right side: ____
Hyperbolic paraboloid