A spheroid is an ellipsoid having two axes of equal length, making it a surface of revolution.
By convention, the two distinct axis lengths are denoted and ,
and the spheroid is oriented so that its axis of rotational symmetric is along the
-axis, giving it the parametric representation

(1)

(2)

(3)

with , and .

The Cartesian equation of the spheroid is

(4)

If , the spheroid is called oblate
(left figure). If ,
the spheroid is prolate (right figure). If , the spheroid degenerates to a sphere.