Parabole de foyer et de directrices quelconques

F = (-12.69151673261407, 9.532748119723193)
a = -0.6 (slider from -5 to 5, step 0.05)
b = 1.35 (slider from -5 to 5, step 0.05)
c = -3.75 (slider from -5 to 5, step 0.05)
eq1: (a * x) + (b * y) + c = 0
g = OrthogonalLine(F, eq1)
F' = Intersect(g, eq1)
I = Midpoint(F, F')
x_{f}: x(F)
y_{f}: y(F)
eq3: (b^(2) * x^(2)) + (a^(2) * y^(2)) - ((((2 * a) * b) * x) * y) - ((2 * ((x_{f} * (a^(2) + b^(2))) + (a * c))) * x) - ((2 * ((y_{f} * (a^(2) + b^(2))) + (b * c))) * y) + ((a^(2) + b^(2)) * (x_{f}^(2) + y_{f}^(2))) - c^(2) = 0