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