Two center bipolar coordinates

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, two-center bipolar coordinates is a coordinate system, based on two coordinates which give distances from two fixed centers, C1 and C2 This system is very useful in some scientific applications It should not be confused with so-called bipolar coordinates. Bipolar coordinates are a two-dimensional orthogonal coordinate system. There are two commonly defined types of bipolar coordinates. The other system is two-center bipolar coordinates. There is also third coordinate system that based on two poles (biangular coordinates). First is based on the Apollonian circles. The curves of constant ¿ and of ¿ are circles that intersect at right angles. The coordinates have two foci F1 and F2, which are generally taken to be fixed at (¿a, 0) and (a, 0), respectively, on the x-axis of a Cartesian coordinate system.