Inverse Curve

Given a Circle with Center and Radius , then two points and are inverse with respect to if . If describes a curve , then describes a curve called the inverse of with respect to the circle (with Inversion Center ). If the Polar equation of is , then the inverse curve has polar equation

If and , then the inverse has equations

References

Lee, X. Inversion.'' http://www.best.com/~xah/SpecialPlaneCurves_dir/Inversion_dir/inversion.html.

Lee, X. Inversion Gallery.'' http://www.best.com/~xah/SpecialPlaneCurves_dir/InversionGallery_dir/inversionGallery.html

Yates, R. C. Inversion.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 127-134, 1952.