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
x2/a2 + y2/b2 + z2/c2 = 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.