a=

b=

Biljarten op een ellipstafel.
(x/p)²+(y/q)²=1  
A(a,0) en B(b,0).  [houd A en B tussen de brandpunten]
Punt P of S op ellips
geeft route A-P-B of A-S-B.

f nodig om 
hoek-inval=hoek-uitval te vinden.
f(x)=0 geeft x=cos(t).
t nodig voor punt P(p.cos(t),q.sin(t)) of S.

grafiek f

hoek t voor S

hoek t voor P

p=

q=

brandpunten

tekst

q = 1 (slider from 0 to 3)
p = 2 (slider from 0 to 3)
b = 0.56 (slider from -2.8 to 2.8)
a = -1.5 (slider from -2.8 to 0)
Invulvak1 = Textfield(a)
Invulvak2 = Textfield(b)
f(x) = ((((((p^(2) - q^(2)) * q^(2)) * (a + b)) * x^(2)) - (((2 * (p * q^(2))) * ((a * b) + p^(2) - q^(2))) * x) + ((p^(2) * q^(2)) * (a + b))) * (b - a))
K, N = Root(f)
c = Circle(N, 1)
L, Q = Intersect(c, yAxis)
α = Angle(Q, N, K)
P: ((p * cos(α)), (q * sin(α)))
A: (a, 0)
B: (b, 0)
i = Segment(B, P)
j = Segment(P, A)
e = Circle(K, 1)
D, E = Intersect(e, yAxis)
δ = Angle(E, K, A)
S: ((p * cos(δ)), (q * sin(δ)))
n = Segment(A, S)
p_1 = Segment(S, B)
r = false
t = false
s_1 = false
Invulvak3 = Textfield(p)
Invulvak4 = Textfield(q)
s: (x / p)^(2) + (y / q)^(2) = 1
tekst2 = LaTeX(s, true, true)
H, I = Focus(c)
F1, F2 = Focus(s)
o = false
g, m = Tangent(P, s)
h = OrthogonalLine(P, g)
C = Intersect(h, xAxis)
β = Angle(A, P, C)
γ = Angle(C, P, B)
k, d = Tangent(S, s)
l = OrthogonalLine(S, k)
F = Intersect(l, xAxis)
ε = Angle(A, S, F)
ζ = Angle(F, S, B)
O = Intersect(xAxis, yAxis)
f_1 = Segment(A, O)
g_1 = Segment(O, B)
u = false