See construction

$\Gamma$

$\vec{\mathbf u}$

$\vec{\mathbf v}$

o = true
P_3 = (4.854243668300081, 5.144971973685039)
P_2 = (2.009394768870981, 2.5919024485563598)
P_1 = (2.3417637891062237, -0.2)
c = Circle(P_1, 2)
A = Point(c)
t = Line(P_1, A)
a = Line(P_2, P_1)
b = Line(P_1, P_3)
d = Line(P_2, P_3)
e = Circle(P_1, P_2, P_3)
B = Center(e)
f = OrthogonalLine(B, t)
J = Mirror(P_1, f)
g = Line(P_1, d)
h = OrthogonalLine(B, g)
K = Mirror(P_1, h)
i = Line(P_3, J)
j = Line(P_2, K)
X = Intersect(i, j)
k = Line(P_2, J)
l = Line(P_3, K)
Y = Intersect(l, k)
m = Line(Y, X)
M, N = Intersect(e, m)
u = Vector(P_1, M)
v = Vector(P_1, N)
p = IPPPC_p(P_1, P_2, P_3, u)
q = IPPPC_p(P_2, P_1, P_3, v)

Tool: Parabola Direccion_eje Punto Tangente_Punto (command ParabolaDireccion_ejePuntoTangente)
Dar un vector (dircción del eje), un punto, una tangente y el punto de tangencia
Input: u, P_1, t_P, P
Output: p

Dirección del eje

P = Point(t_P)
b = Line(P, u)
c = Line(P_1, u)
d = Circle(P_1, P)
E, F = Intersect(d, c)
e = AngularBisector(E, P_1, P)
G = Intersect(e, b)
H = Intersect(t_P, c)
f = Segment(H, G)
g = Line(P, f)
I = Intersect(e, g)
h = AngularBisector(P, P_1, F)
J = Intersect(b, h)
i = Segment(H, J)
j = Line(P, i)
K = Intersect(h, j)
k = AngularBisector(I, P_1, P)
L = Intersect(b, k)
l = Segment(H, L)
m = Line(P, l)
O = Intersect(k, m)
p = Conic(P_1, I, O, P, K)

Tool: IPPPC_p
Dar tres puntos y un vector
Input: P_1, P_2, P_3, u
Output: g

Dirección del eje

Recta de Pascal

c = Line(P_2, P_1)
b = Line(P_2, P_3)
d = Line(P_3, u)
a = Line(P_1, u)
C = Intersect(b, a)
e = Line(C, c)
D = Intersect(e, d)
t_1 = Line(D, P_1)
g = ParabolaDireccion_ejePuntoTangente(u, P_2, t_1, P_1)