In oblique coordinates the general equation of a circle is x� + 2xy cos ω + y� + 2Ax + 2By + C = 0.

It follows that the product xy is constant, and since x and y are the oblique coördinates of the point P, the asymptotes being the axes of reference, we have The equation of the hyperbola, referred to the asymptotes as axes, is xy = constant.