Cónicas dados un foco, un punto y dos tangentes

Mostrar la construcción

P(PF)

j = true
A = (2.1581269663449203, -3.6186721507691497)
B = (12.935583210867518, 4.7250980721645695)
t_1 = Line(A, B)
C = (-0.35877240301016866, 7.087541584547295)
D = (19.212937618392836, -0.5758535102055287)
t_2 = Line(C, D)
F = (8.076728679064306, -2.9768380378652703)
P = (12.17772961606694, -5.264764876403583)
S_1 = Mirror(F, t_1)
S_2 = Mirror(F, t_2)
c = Circle(P, F)
d = Circle(S_1, S_2, F)
E = Intersect(t_1, t_2)
a = Line(E, P)
b = OrthogonalLine(F, a)
e = Line(S_1, S_2)
R = Intersect(b, e)
H = Midpoint(R, P)
f = Circle(H, P)
I, J = Intersect(f, c)
h = Circle(S_1, S_2, I)
F_I = Center(h)
M = Midpoint(F, F_I)
t = Circle(M, Distance[F_I, S_1] / 2)
P'_1 = Mirror(P, M)
m = Line(F_I, F)
P' = Mirror(P, m)
Q, S = Intersect(t, m)
c_1 = Conic(P, S, P', P'_1, Q)
g = Circle(S_1, S_2, J)
F_J = Center(g)
i = Line(F_J, F)
P'_2 = Mirror(P, i)
s = Parabola(F, e)
G = Midpoint(F, F_J)
P'_3 = Mirror(P, G)
k = Circle(G, Distance[F_J, S_1] / 2)
K, L = Intersect(k, i)
p = Conic(P, K, P'_2, P'_3, L)

Tool: Conica Foco Punto Dos Tangentes (command ConicaFocoPuntoDosTangentes)
Dar un foco, un punto y dos tangentes
Input: F, P, t_1, t_2
Output: k, q, p, r

S_1 = Mirror(F, t_1)
S_2 = Mirror(F, t_2)
c = Circle(P, F)
E = Intersect(t_1, t_2)
a = Line(E, P)
b = OrthogonalLine(F, a)
e = Line(S_1, S_2)
R = Intersect(b, e)
H = Midpoint(R, P)
f = Circle(H, P)
I, J = Intersect(f, c)
g = Circle(S_1, S_2, J)
h = Circle(S_1, S_2, I)
K = Center(g)
L = Center(h)
k = Ellipse(F, L, P)
p = Hyperbola(F, L, P)
q = Ellipse(F, K, P)
r = Hyperbola(F, K, P)