Ellipsoid

Ellipsoid is a family of surfaces that can be described by this equation:

sshot 2026-04-14 3477f
sshot 2026-04-14 3477f
With[{a = 2, b = 1.5, c = 3},
 ParametricPlot3D[
{a*Cos[u]*Sin[v], b*Sin[u]*Sin[v], c*Cos[v]},
{u, 0, Pi}, {v, 0, 2*Pi},
 BoundaryStyle -> {Thin, Black},
 PlotStyle -> Directive[RandomColor[], Opacity[0.7],
 Specularity[White, 30]]]]

It is called ellipsoid because the cross section alone the axes of the surface are ellipses, and the equation's form is the 3D analogue of the equation for ellipses.

Conic Section Surfaces