Cassini oval

A Cassini oval, also called a Cassinian curve or oval of Cassini, is a quartic plane curve defined as the locus of points whose distances from two fixed points, the foci, have a constant product. It can be set against the ellipse, where the sum of the distances is constant. The shape depends on the ratio of the constant to half the distance between the foci: when the ratio is below one the curve has two separate loops, one around each focus; at exactly one it becomes the lemniscate of Bernoulli, a sideways figure eight; and above one it is a single loop around both foci, peanut shaped at first and then convex, tending to a circle as the foci merge. The curves are the special case of polynomial lemniscates of degree two. They are named after Giovanni Domenico Cassini, who studied them in the late seventeenth century and proposed them as the paths of planets around the sun in place of Kepler's ellipses.