Conchoid of Nicomedes

Draw every line through a point O, and on each mark the two points at a fixed distance d from where it crosses a fixed straight line. The marks make two branches that close in on that line, and when d is more than O’s distance from the line the inner branch has a loop. It can trisect an angle, and its name is from the Greek for shell-like.

x = a ± d cos θ, y = a tan θ ± d sin θ

On mathcurve.com as Conchoïde de Nicomède