Bicorn

In geometry, the bicorn, also known as a cocked hat curve due to its resemblance to a bicorne, is a rational quartic curve defined by the equation^[1] $${\displaystyle y^{2}\left(a^{2}-x^{2}\right)=\left(x^{2}+2ay-a^{2}\right)^{2}.}$$ It has two cusps and is symmetric about the y-axis.^[2]