Cónica dada por cinco puntos

Mostar la construcción

a = true
P_1 = (7.6310079086779945, -0.7322248830410591)
P_2 = (11.9, 2.14)
P_3 = (20.74, -0.14)
P_4 = (12, -5.54)
P_5 = (9.56, -4.36)
A_1 = (6.10856560539607, -5.251975470909259)
c = Circle(P_5, A_1)
Q = Point(c)
δ = Line(P_5, Q)
b = Line(P_1, P_2)
f = Line(P_4, P_5)
L = Intersect(b, f)
d = Line(P_2, P_3)
M = Intersect(δ, d)
e = Line(P_3, P_4)
RectaPascal = Line(M, L)
N = Intersect(e, RectaPascal)
C_1: N
g = Line(P_1, C_1)
P = Intersect(δ, g)
k = Conic(P_1, P_2, P_3, P_4, P_5)

Tool: Conica foco tres tangentes (command Conicafocotrestangentes)
Primero se señala el foco y luego las tres tangentes
Input: F, t_1, t_2, t_3
Output: e, O, F'

S_3 = Mirror(F, t_3)
S_2 = Mirror(F, t_2)
S_1 = Mirror(F, t_1)
c = Circle(S_1, S_2, S_3)
F' = Center(c)
a = Line(S_1, F')
b = Line(S_3, F')
d = Line(F', S_2)
P_1 = Intersect(t_1, a)
P_3 = Intersect(t_3, b)
P_2 = Intersect(t_2, d)
O = Midpoint(F, F')
I' = Mirror(P_2, O)
G' = Mirror(P_1, O)
e = Conic(P_1, P_2, P_3, I', G')