Elliptic Coordinates

Parabolic Coordinates

Bipolar Coordinates

Confocal Ellipsoidal Coordinates in 3D space

Ellipsoids (white),

Hyperboloids of one sheet (orange) and

Hyperboloids of two sheets (yellow)

References:

The first three figures are scanned from

“Mathematical Methods for Physicists” by Arfken

The color figure is my coloring of a figure from one of my “Desert Island Books”:

“Geometry and the Imagination” by Hilbert and Cohn-Vossen.

The ultimate reference for this kind of stuff is

“Methods of Theoretical Physics” by Morse and Feshbach.