Parábola dada por cuatro tangentes

Mostar la construcción

m = true
I = (-5.580904396952118, 1.1017689821078294)
J = (11.41371360429877, -6.075596605319339)
t_1 = Line(I, J)
G = (22.220970682764143, -0.21820629833854854)
H = (-0.053528639263721985, -6.611836563000679)
t_2 = Line(G, H)
C = (-1.0435063869094048, -4.343129049733471)
D = (2.3389175842133447, 12.569054230985719)
t_3 = Line(C, D)
A_1 = (2.9989027493104667, -7.973061070961005)
B = (-0.7960119499979841, 9.970352897606917)
t_4 = Line(A_1, B)
E = Intersect(t_2, t_1)
F_1 = Intersect(t_4, t_3)
L = Intersect(t_4, t_1)
a = Line(E, t_3)
b = Line(F_1, t_2)
W_5 = Intersect(a, b)
c = Line(L, W_5)
d = Line(F_1, E)
e = Line(L, t_2)
M = Intersect(e, d)
f = Line(M, t_3)
P_1 = Intersect(t_1, f)
g = Line(P_1, c)
h = OrthogonalLine(P_1, t_1)
g' = Mirror(g, h)
i = Line(L, t_3)
O = Intersect(d, i)
j = Line(O, t_2)
P_4 = Intersect(t_4, j)
k = Line(P_4, c)
l = OrthogonalLine(P_4, t_4)
k' = Mirror(k, l)
F = Intersect(g', k')
S_4 = Mirror(F, t_4)
S_1 = Mirror(F, t_1)
directriz = Line(S_4, S_1)
p = Parabola(F, directriz)
Q = Intersect(a, e)
n = Line(F_1, Q)
P_2 = Intersect(t_2, n)
S = Intersect(b, i)
q = Line(E, S)
P_3 = Intersect(t_3, q)
eje = OrthogonalLine(F, directriz)
N = Intersect(directriz, eje)
A = Midpoint(F, N)

Tool: Parabola CuatroTangentes (command ParabolaCuatroTangentes)
Dar cuatro tangentes
Input: t_1, t_2, t_3, t_4
Output: p, F, directriz

E = Intersect(t_2, t_1)
F_1 = Intersect(t_4, t_3)
L = Intersect(t_4, t_1)
a = Line(E, t_3)
b = Line(F_1, t_2)
W_5 = Intersect(a, b)
c = Line(L, W_5)
d = Line(F_1, E)
e = Line(L, t_2)
M = Intersect(e, d)
f = Line(M, t_3)
P_1 = Intersect(t_1, f)
g = Line(P_1, c)
h = OrthogonalLine(P_1, t_1)
g' = Mirror(g, h)
i = Line(L, t_3)
O = Intersect(d, i)
j = Line(O, t_2)
P_4 = Intersect(t_4, j)
k = Line(P_4, c)
l = OrthogonalLine(P_4, t_4)
k' = Mirror(k, l)
F = Intersect(g', k')
S_4 = Mirror(F, t_4)
S_1 = Mirror(F, t_1)
directriz = Line(S_4, S_1)
p = Parabola(F, directriz)