Kampyle of Eudoxus

Kampyle is Greek for curved, and Eudoxus of Cnidus studied this quartic for the problem of doubling the cube. Take a point P on a circle about O and let the tangent there meet the axis at Q: the curve passes where the line OP crosses the vertical through Q. Its four arms open out along two parabolas, drawn dashed.

x⁴ = a²(x² + y²)

On mathcurve.com as Campyle d’Eudoxe