Ανακλαστική Ιδιότητα Παραβολής
Author: Μπουμπούλης Παντελής

PLAY

y_0 = 3.5 (slider from -5 to 5, step 0.1)
p = 4.2 (slider from 0 to 5, step 0.1)
P: (y_0^(2.0) / (2.0 * p), y_0)
E: (p / 2.0, 0.0)
R = Segment(E, P)
d: sqrt(R^(2.0) - y_0^(2.0))
sinus: d / R
t = 0 (slider from 0 to 3, step 0.01)
x_0 = 7.2 (slider from 0 to 10, step 0.1)
param_3: R / (x_0 - y_0^(2.0) / (2.0 * p))
param_2: (p / 2.0 - y_0^(2.0) / (2.0 * p)) / sinus
c: y^(2.0) = 2.0 * p * x
f = Function(y_0, y_0^(2.0) / (2.0 * p), Infinity)
a: (y_0 - 0.0) / (y_0^(2.0) / (2.0 * p) - p / 2.0)
g(x) = a * (x - p / 2.0)
x_1: y_0^(2.0) / (2.0 * p) + (t - 1.0) * sinus * param_2
A_0: (x_0, y_0)
param_1: x_0 - y_0^(2.0) / (2.0 * p)
A = If(t ≤ 1.0, (x_0 - t * param_1, y_0), If[t ≤ 2.0, (x_1, g(x_1))])
x_2: y_0^(2.0) / (2.0 * p) + (t - 1.5) * sinus * param_2
x_3: y_0^(2.0) / (2.0 * p) + (t - 2.0) * sinus * param_2
B = If(t > 0.5, If[t < 1.5, (x_0 - (t - 0.5) * param_1, y_0), If[t < 2.5, (x_2, g(x_2))]])
C = If(t > 1.0, If[t < 2.0, (x_0 - (t - 1.0) * param_1, y_0), If[t ≤ 3.0, (x_3, g(x_3))]])