Orthogonal Trajectories in Vectorial Coordinates

Extract

The position of a point in a plane may be determined by its distances (r, ρ) from two fixed points which may be termed foci. These distances are termed vectorial coordinates. The determination is unique if attention is confined to the half-plane bounded by the line of foci. In certain cases where the properties of a curve are defined with respect to two points, representation of the curve by an equation between its vectorial coordinates possesses certain advantages. For example, the equation of the ellipse takes the extremely simple form r + p = 2α.