Cardioid Cartesian equation: (x 2 + y 2 - 2ax) 2 = 4a 2 (x 2 + y 2) Polar equation: r = 2a(1 + cos θ)) Click below to see one of the Associated curves. Definitions of the Associated curves Evolute Involute 1 Involute 2 Inverse curve wrt origin Inverse wrt