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GRANVILLE EGG
Curve considered by Granville in 1908. 
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