Conchoid of de Sluze

A curve first constructed by René de Sluze in 1662. In Cartesian Coordinates,

$$a(x-a)(x^2+y^2)=k^2x^2,$$

and in Polar Coordinates,

$$r={k^2\cos\theta\over a}+a\sec\theta.$$

The above curve has $k^2/a=1$, $a=-0.5$.