Parallels of cardioid.
Inversion curves of a cardioid {-2 Sin[t] - Sin[2 t], 2 Cos[t] + Cos[2 t]} with respect to points on the line x==0 and inversion circle radius 2.
From top to bottom, left to right: Inversion curves of the cardioid with respect to points on the line y==0, y==1, y==2, and y==4 respectively. The inversion circle has radius 2.
Pedal curves of cardioid, with respect to points on the line x==0 (left figure) and x==y (right figure)