polaires

Involution de O*

directions fixes

détail M

F = Point(xAxis)
O = Intersect(xAxis, yAxis)
F' = Mirror(F, O)
S = Point(xAxis)
Γ = If(Distance[O, F] < Distance[O, S], Ellipse[F, F', S], Hyperbola[F, F', S])
ff' = Line(F, F')
oy = OrthogonalLine(O, ff')
F_b = (-1.5037491397998615, 1.4757030891558283)
ff'_b = Line(F_b, O)
S_b = Point(ff'_b)
F'_b = Mirror(F_b, O)
Γ_b = If(Distance[O, F_b] < Distance[O, S_b], Ellipse[F_b, F'_b, S_b], Hyperbola[F_b, F'_b, S_b])
oy_b = OrthogonalLine(O, ff'_b)
s1 = false
s2 = false
s3 = false
M = (-3.129123831849432, 1.9125559327684096)
N = (0.3668694605823549, 3.524184046300794)
p_M = Polar(M, Γ)
p_Mb = Polar(M, Γ_b)
M' = Intersect(p_M, p_Mb)
p_N = Polar(N, Γ)
p_Nb = Polar(N, Γ_b)
N' = Intersect(p_N, p_Nb)
om = Line(O, M)
om' = Line(O, M')
on = Line(O, N)
on' = Line(O, N')
w = (2.8462973275552463, 2.309264391484072)
c_W = Circle(w, O)
m = Mirror(O, OrthogonalLine[w, om])
m' = Mirror(O, OrthogonalLine[w, om'])
n' = Mirror(O, OrthogonalLine[w, on'])
n = Mirror(O, OrthogonalLine[w, on])
mn' = Line(m, n')
m'n = Line(m', n)
V = Intersect(mn', m'n)
mn = Line(m, n)
m'n' = Line(m', n')
U = Intersect(mn, m'n')
uv = Line(U, V)
u, v = Intersect(c_W, uv)
ou = Line(O, u)
ov = Line(O, v)
A, C = Intersect(Γ, ov)
D, B = Intersect(Γ, ou)
mf = Line(M, F)
mf' = Line(M, F')
M_1, M_2 = Intersect(Γ, mf)
M_3, M_4 = Intersect(Γ, mf')
m1m3 = Line(M_1, M_3)
m2m4 = Line(M_2, M_4)
m1m4 = Line(M_1, M_4)
m2m3 = Line(M_3, M_2)
I = Intersect(m1m4, m2m3)
J = Intersect(m1m3, m2m4)
a = false