Elliptic coordinate system

In geometry, the elliptic coordinate system is a two-dimensional orthogonal coordinate system in which the coordinate lines are 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.