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Bipolar cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional bipolar coordinate system in theperpendicular z {\displaystyle z} -direction. The two lines of foci F 1 {\displaystyle F_{1}} and F 2 {\displaystyle F_{2}} of the projected Apollonian circles are generally taken to be defined by x = − a {\displaystyle x=-a} and x = + a {\displaystyle x=+a} , respectively, in the Cartesian coordinate system.
The term "bipolar" is often used to describe other curves having two singular points , such as ellipses, hyperbolas, and Cassini ovals. However, the term bipolar coordinates is never used to describe coordinates associated with those curves, e.g., elliptic coordinates.