The locus of the Gigoujeu scenario is 2 2 2 2 2 2 2 2 4 2 3 2 2 2 2 y + a - R a y - 2 y R + y R + x - 2 x a + 4 x a - 2 x R - 2 a x 4 2 3 3 3 2 4 2 2 2 2 3 2 4 + x a - 2 x a + 2 x a R + a x - 2 x R a - 2 a x + x R 2 2 2 2 2 2 2 + 2 x R a - 2 a y x + 2 a y x R + a y x = 0 and in Maple input format y^2+a^2-R^2*a^2*y^2-2*y^2*R^2+y^2*R^4+x^2-2*x^3*a+4*x^2*a^2-2*x^2*R^2-2*a*x+x^4 *a^2-2*x^3*a^3+2*x^3*a*R^2+a^4*x^2-2*x^2*R^2*a^2-2*a^3*x+x^2*R^4+2*x*R^2*a-2*a* y^2*x+2*a*y^2*x*R^2+a^2*y^2*x^2 = 0 This took, 0.113, seconds .