Elliptic Paraboloid

A quadratic surface which has elliptical cross section. The elliptic paraboloid of height , semimajor axis , and semiminor axis can be specified parametrically by

			(1)
			(2)
			(3)

for and .

This gives first fundamental form coefficients of

			(4)
			(5)
			(6)

second fundamental form coefficients of

			(7)
			(8)
			(9)

The Gaussian curvature and mean curvature are

			(10)
			(11)

The Gaussian curvature can be expressed implicitly as

(12)