P = (5.02, 1.18)
U = (1.4677514219690615, 3.4730551506788685)
A_1 = (4.580717002262266, 4.192922315048012)
B_1 = (3.7231467039558024, -0.09156958768065963)
u = Line(A_1, B_1)
V = (2.2268844681011846, 1.1186425148488088)
C_1 = (2.9885619601744917, 4.176947515294621)
D_1 = (5.637716252611506, -0.18949775063170918)
v = Line(C_1, D_1)
a = Line(U, P)
A = Intersect(a, u)
P_2 = ConjugadoArmonico(U, A, P)
b = Line(V, P_2)
B = Intersect(b, v)
P_3 = ConjugadoArmonico(V, B, P_2)
d = Line(U, P_3)
C = Intersect(u, d)
P_4 = ConjugadoArmonico(U, C, P_3)
c = Line(V, P)
D = Intersect(c, v)
P_5 = ConjugadoArmonico(V, D, P)
e = Conic(P, P_2, P_3, P_4, P_5)

Tool: Conjugado Armonico (command ConjugadoArmonico)
Dar dos puntos A, B y un punto sobre AB, determina D, tal que (CD;AB)=-1
Input: A, B, C
Output: D

a = Line(A, B)
O = Midpoint(A, B)
c = Circle(O, A)
b = Polar(C, c)
D = Intersect(a, b)

Tool: Pp_Qp_Q (command PpQpQ)
Dar P,, un punto y su polar, un punto y su polar
Input: P, U, u, V, v
Output: e, P_2, P_3, P_4, P_5

a = Line(U, P)
A = Intersect(a, u)
P_2 = ConjugadoArmonico(U, A, P)
b = Line(V, P_2)
B = Intersect(b, v)
P_3 = ConjugadoArmonico(V, B, P_2)
d = Line(U, P_3)
C = Intersect(u, d)
P_4 = ConjugadoArmonico(U, C, P_3)
c = Line(V, P)
D = Intersect(c, v)
P_5 = ConjugadoArmonico(V, D, P)
e = Conic(P, P_2, P_3, P_4, P_5)