Der Parameter m verändert den Berührpunkt, a und b die Form der Hyperbel

a = 2.5 (slider from 0 to 5, step 0.1)
b = 1.5 (slider from 0 to 5, step 0.1)
f_+(x) = b / a * sqrt(x^(2.0) - a^(2.0))
f_-(x) = -(b) / a * sqrt(x^(2.0) - a^(2.0))
g_-(x) = -(b) / a * sqrt(x^(2.0) + a^(2.0))
g_+(x) = b / a * sqrt(x^(2.0) + a^(2.0))
m = 2 (slider from -5 to 10, step 0.1)
t: sqrt(a^(2.0) * m^(2.0) - b^(2.0))
B_1: (-a^(2.0) * m / t, -a^(2.0) * m^(2.0) / t + t)
B_2: (a^(2.0) * m / t, -(-a^(2.0) * m^(2.0) / t + t))
c: y = b / a * x
d: y = -(b) / a * x
e: y = m * x
A = Intersect(g_+, e, (0.7862136267227171, 1.5724272549355074))
B = Intersect(g_-, e, (-0.7862136267227171, -1.5724272549355074))
B_5: ((a^(2.0) * m * sqrt(3.0) / 2.0 * t + a * b * t / 2.0) / (-t^(2.0)), -(m) / t^(2.0) * (a^(2.0) * m * sqrt(3.0) / 2.0 * t + a * b * t / 2.0) + sqrt(3.0) / 2.0 * t)
B_6: ((a^(2.0) * m * sqrt(3.0) / 2.0 * t - a * b * t / 2.0) / (-t^(2.0)), -(m) / t^(2.0) * (a^(2.0) * m * sqrt(3.0) / 2.0 * t - a * b * t / 2.0) + sqrt(3.0) / 2.0 * t)
f = Conic(B_2, A, B_1, B_5, B)
g: y = m * x + t
h: y = m * x
i: y = m * x - t
j: y = m * x + sqrt(3.0) / 2.0 * t
O = (0, 0)
k = FirstAxis(f)
l, s = Tangent(A, f)
n, a_1 = Tangent(B, f)
p = OrthogonalLine(O, k)
C, D = Focus(f)