P=(y(B_x),y(A_y))

y^2=a\, x^3

x=t^2

y=a\, t^3

Haftendorn, Buch:
Kurven erkunden und verstehen
Kap 4.2:S. 91, Ergänzung 

Ha 2016

t = 0.66 (slider from -3 to 3, step 0.01)
T: (t, 0)
s = OrthogonalLine(T, xAxis)
a = 1 (slider from -5 to 5, step 1)
g(x) = (a * x^(3))
xpq: (a^(2) * (t + t^(2)))
ypq: (a^(2) * (t - t^(2)))
xp: sqrt(xpq)
yp: sqrt(ypq)
P_1: (xp, yp)
O = (0, 0)
P' = Mirror(P_1, O)
B_x, A_x = Intersect(c, s)
A_y = Intersect(g, s)
P: (y(B_x), y(A_y))
Ortslinie1 = Locus(P, t)
f: y = y(A_y)
b: y^(2) = (a^(2) * x^(3))
h: y = y(A_y)
i: y = x
j: y = y(B_x)
A = Intersect(j, i)
B = Point(j)
k = Ray(A, B)
l = OrthogonalLine(A, xAxis)
u = Vector(B, A)
v = Vector(A, P)
d = false
Text6 = LaTeX(B, true, true)