The Granville egg is the hyperbolism of a circle with centre B with respect to a point O and a line (D) perpendicular to (OB) Parameter for the opposite curve: a = 4, b = 5, r = 1.

Cartesian equation for B(b, 0),  (D) : x = a and a circle with radius r: . Cartesian parametrization: . Rational quartic.

Case a = b= 2r	When r = b = a/2, this quartic is composed of the witch of Agnesi and the abscissa axis	When r = a, b = 0, we get the Külp quartic

Other ovoid quartic:, opposite case a = 3, b = 2, c = 1/4 (proposed by Massimo Vaglieco).

Compare to the Rosillo curves and see other eggs at ovoid.

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© Robert FERRÉOL  2017