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Elliptic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional elliptic coordinate system in theperpendicular z {\displaystyle z} -direction. Hence, the coordinate surfaces are prisms of confocal ellipses and hyperbolae. The two foci F 1 {\displaystyle F_{1}} and F 2 {\displaystyle F_{2}} are generally taken to be fixed at − a {\displaystyle -a} and + a {\displaystyle +a} , respectively, on the x {\displaystyle x} -axis of the Cartesian coordinate system.
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