r=c\,e^{a\, \theta}

r_i=\frac{k^2}{c} ℯ ^{-a \,\theta}

https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 9.5.6.2  S.295 Afg. 9.17
www.kurven-erkunden-und-verstehen.de

Ha 2017

anf = -15
a = 0.158 (slider from -5 to 5, step 0.01)
c = 0.5 (slider from -5 to 5, step 0.01)
r(x) = (c * ℯ^((a * x)))
h = CurveCartesian((r(t) * cos(t)), (r(t) * sin(t)), t, anf, 20)
endinv = 9
anfinv = 3
k = 1 (slider from 0 to 3, step 0.1)
g(x) = (k^(2) / c * exp(((-a) * x)))
ende = 3.9 (slider from -5 to 20, step 0.01)
A = Intersect(xAxis, yAxis)
invk = Circle(A, k)
b = CurveCartesian((r(t) * cos(t)), (r(t) * sin(t)), t, anf, ende)
end: ((-log(c))) / a
O: (0, 0)
m' = Mirror(b, yAxis)
Q = Point(h)
Q' = Mirror(Q, yAxis)
b' = Mirror(b, invk)
f: 2.43
m'' = Dilate(m', f, O)
Q'' = Dilate(Q', f, O)
e = CurveCartesian((g(u) * cos(u)), (g(u) * sin(u)), u, anfinv, endinv)
f_t: (k^(2) / c^(2) * ℯ^(((-a) * π)))
P = Mirror(Q, invk)
d = false