Cayley's Sextic

Cartesian equation:
4(x2+y2ax)3=27a2(x2+y2)24(x^{2} + y^{2} - ax)^{3} = 27a^{2}(x^{2} + y^{2})^{2}
Polar equation:
r=4acos3(θ/3)r = 4a \cos^{3}( \theta /3)


This was first discovered by Maclaurin but studied in detail by Cayley.

The name Cayley's sextic is due to R C Archibald who attempted to classify curves in a paper published in Strasbourg in 1900.

The evolute of Cayley's Sextic is a nephroid curve.