Ellipsoid

Ellipsoid

12.1 Planes and surfaces

12.2 Graphs and level curves
14.6 Surface integrals

Note: Section numbers refers to Calculus, Early Transcendentals (2nd edition) by Briggs, Cochran, and Gillett.

The surface defined by the equation

is an Ellipsoid. Here are the level sets of constant height. The level sets are ellipses - hence the name of the shape!

The following object shows a polar parameterization of an ellipsoid given below with the parameters t and z. This surface can be used in discussion of parametrization of surfaces. The horizontal curves are curves of fixed z. The vertical curves represent the fixed t.