The Bipararola

A curve of class three having the line at infinity as a bitangent in two perpendicular directions has a straight line for its orthoptic locus. This curve has been identified in this paper as the negative pedal of a rectangular hyperbola with respect to a point on itself. The Cartesian equation of the curve is obtained and the curve is shown to possess properties remarkably analogous to those of the parabolat a fact, first pointed out by Mr. A. Narasinga Rao The curve has been named the harmonic biparabola The name biparabola has been chosen as being shorter ihan the term " two-fold parabola " used by Clifford,↓ who gives also a method of generation Other methods of generating the curve are also indicated in the paper.