Talbot’s curve

Through each point of an ellipse draw the line square to the radius from the centre; together the lines wrap Talbot’s curve. For an ellipse flat enough that e² > 1/2 it has four cusps and two double points, as here, and for a rounder one it is an oval. Halved, it is the set of centres of the circles that pass through the ellipse’s centre and touch the ellipse.

x = a cos t (1 + e² sin² t), y = a sin t (1 - 2e² + e² sin² t)/√(1 - e²)

On mathcurve.com as Courbe de Talbot