Uploaded Jan 19, 2014

The purple curve has polar equation r=f(θ).

A lies on this curve, and B is a point at the intersection of the tangent at A with the line perpendicular to OA.

The red curve is the locus of B

The grey curve is the curve r=g(θ) rotated by the quantity on the slider.

What function g() will rotate to lie on top of the red curve?