Ellipsi puutuja moodustab puutepunktist tõmmatud fokaalraadiustega võrdsed nurgad

Ellipsi ühest fookusest väljunud ja ellipsilt peegeldunud kiired lõikuvad ellipsi teises fookuses.

α

eXPshOW

β

a = 5 (slider from 0 to 10, step 0.1)
b = 3 (slider from 0 to 10, step 0.1)
c2: sqrt(a^(2) - b^(2))
F_2: (c2, 0)
c: x^(2) / a^(2) + y^(2) / b^(2) = 1
P_0 = Point(c)
x_0: x(P_0)
y_0: y(P_0)
f: (x * x_0 / a^(2)) + (y * y_0 / b^(2)) = 1
j = OrthogonalLine(F_2, f)
A_2 = Intersect(f, j)
c1: (-sqrt(a^(2) - b^(2)))
F_1: (c1, 0)
i = OrthogonalLine(F_1, f)
A_1 = Intersect(f, i)
r_1 = Segment(F_1, P_0)
r_2 = Segment(F_2, P_0)
β = Angle(F_2, P_0, A_2)
α = Angle(A_1, P_0, F_1)
tekst1: "∡α =" + (LaTeX[α]) + " \;   \; ∡β = " + (LaTeX[β]) + ""
d_1 = Segment(F_1, A_1)
d_2 = Segment(F_2, A_2)
c' = Mirror(c, f)
F_1' = Mirror(F_1, f)
F_2' = Mirror(F_2, f)
r_1' = Segment(F_1', P_0)
γ = Angle(F_1', P_0, A_1)
Export_1: (-6.1, 9.8)
Export_2 = (5.1462774548020285, -3.147933733997562)
d = false
A = Mirror(F_2, f)
B = Mirror(P_0, f)
r_2' = Segment(A, B)
δ = Angle(A_2, P_0, F_2')