Bicorn

Cartesian equation: y2(a2 - x2) = (x2 + 2ay - a2)2

The bicorn (also called the cocked-hat) is the name of a collection of quartic curves studied by Sylvester in 1864. The same curves were the studied by Cayley in 1867.

The particular bicorn given by Sylvester and Cayley is a different quartic from the one given here but this one, with a simpler formula, has essentially the same shape.