# ellipsoid

An ellipsoid is a quadratic surface that is the three-dimensional analog of an ellipse. The general equation of an ellipsoid in Cartesian coordinates is

*x*^{2}/*a*^{2} + *y*^{2}/*b*^{2} + *z*^{2}/*c*^{2} = 1

where *a*, *b* and *c* are positive real numbers determining
the shape. If two of these numbers are equal, the ellipsoid is a spheroid;
if all three are equal, it is a sphere. The
intersection of an ellipsoid with a plane is a single point or an ellipse.
Ellipsoids can also be defined in higher dimensions.