f: y = 0
F = Point(f)
F' = Point(f)
C = (-4.7099077585305515, 10.693844940108152)
c = Hyperbola(F, F', C)
P = Point(f)
O = Midpoint(F, F')
g, h = Asymptote(c)
i = OrthogonalLine(P, g)
H = Intersect(g, i)
j = OrthogonalLine(H, f)
P_2, P_1 = Intersect(c, j)
n_1 = OrthogonalLine(P_1, Tangent[P_1, c])
n_2 = OrthogonalLine(P_2, Tangent[P_2, c])