Ziehe beliebig an A und B.
Der Winkel bei S ist stets ein rechter.

https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 7.7.2  S. 214
www.kurven-erkunden-und-verstehen.de

Ha 2017

a_e

b_e

a_h

F_1 = Point(xAxis)
F_2 = Mirror(F_1, yAxis)
B = (0, 3)
c = Ellipse(F_1, F_2, B)
A = (2, 0)
d = Hyperbola(F_1, F_2, A)
C, S, E, F = Intersect(c, d)
f = Tangent(S, c)
g = Tangent(S, d)
G = Point(f)
H = Point(g)
α = Angle(G, S, H)
e: x(F_2)
m_f = Slope(f)
m_g = Slope(g)
senk: (m_f * m_g)
Text2: "m_f*m_g=" + (LaTeX[m_f]) + "*" + (LaTeX[m_g]) + "=" + (LaTeX[senk]) + ""
b_e = SecondAxisLength(c)
a_h = FirstAxisLength(d)
O = Intersect(xAxis, yAxis)
A' = Mirror(A, yAxis)
j = OrthogonalLine(A', xAxis)
k = Circle(O, F_1)
I, J = Intersect(k, j)
l = Segment(I, O)
p = CircleArc(O, F_1, I)
n = false
B_e: (0, b_e)
h = Segment(F_1, B_e)
i = Segment(B_e, O)
A_h: ((-a_h), 0)
m = Segment(A_h, O)
b_h = Segment(A_h, I)