(x^2/a^2) + (y^2/b^2) + (z^2/c^2) = 1

Ellipsoid

*All signs are positive

*Always =1

(x^2/a^2) + (y^2/b^2) - (z^2/c^2) = 1

Hyperboloid of one sheet

*Two signs are positive, one is negative

*Always =1

(x^2/a^2) - (y^2/b^2) - (z^2/c^2) = 1

Hyperboloid of two sheets

*One sign is positive, two are negative

*Always =1

(x^2/a^2) + (y^2/b^2) - (z^2/c^2) = 0

Elliptic Cone

*Two signs are positive, one is negative

*Always =0

z = (x^2/a^2) + (y^2/b^2)

Elliptic Paraboloid

*Both signs are either positive or negative

*Z is always a single variable

z = (x^2/a^2) - (y^2/b^2)

Hyperbolic Paraboloid

*One sign is positive, the other is negative

*Z is always a single variable