Bifolium

A bifolium is a quartic plane curve with equation in Cartesian coordinates:


 * $$(x^2 + y^2)^2 = ax^2y.$$

Construction and equations
Given a circle C through a point O, and line L tangent to the circle at point O: for each point Q on C, define the point P such that PQ is parallel to the tangent line L, and PQ = OQ. The collection of points P forms the bifolium.

In polar coordinates, the bifolium's equation is
 * $$\rho = a \sin\theta \cos^2\theta.$$

For a = 1, the total included area is approximately 0.10.