Cónica: dado un vértice (en el eje focal) , una directriz y un punto

$A$

$d$

$P$

$Q$

$\Phi$

$\mbox{Polar de } Q \mbox{ resp, }\Phi$

$R$

$\Gamma$

Eje focal

$F_1$

$F_2$

$D$

$\mbox{Polar de } A \mbox{ resp. } \Psi$

$A_2$

$O_2$

$F'_2$

$ \fbox{\mbox{Elipse}} $

$ \fbox{Hipérbola} $

$A_1$

$O_1$

$F'_1$

$ \fbox{Hipérbola} $

$ \fbox{Elipse} $

$P'$

A = (2.602906620696744, -0.4378289361894402)
B = (-11.056569050919359, 7.734753759513239)
C = (-11.22983935542189, -4.076505330742579)
d = Line(B, C)
P = (-3.317162116473027, 2.82542846527488)
b = Line(P, A)
Q = Intersect(d, b)
E = Midpoint(A, P)
ϕ = Circle(E, A)
e = Polar(Q, ϕ)
R = Intersect(b, e)
G = Midpoint(R, Q)
Γ = Circle(G, Q)
a = OrthogonalLine(A, d)
F_1, F_2 = Intersect(Γ, a)
D = Intersect(d, a)
K = Midpoint(F_2, D)
ψ = Circle(K, D)
h = Polar(A, ψ)
i = Polar(A, ψ)
A_2 = Intersect(a, h)
O_2 = Midpoint(A, A_2)
F'_2 = Mirror(F_2, O_2)
k = Ellipse(F_2, F'_2, P)
p = Hyperbola(F_2, F'_2, P)
D_1 = Midpoint(F_1, D)
c = Circle(D_1, F_1)
f = Polar(A, c)
A_1 = Intersect(f, a)
O_1 = Midpoint(A_1, A)
F'_1 = Mirror(F_1, O_1)
g = Hyperbola(F_1, F'_1, P)
q = Ellipse(F_1, F'_1, P)
P' = Mirror(P, a)

Tool: Conica Punto Tangente Tangente_Punto (command ConicaPuntoTangenteTangente_Punto)
Dar el foco, dos tangentes y el punto de contacto de la última
Input: F, t, t_P, P
Output: e, g, f, F_2

P = Point(t_P)
S_1 = Mirror(F, t)
S_2 = Mirror(F, t_P)
a = Line(S_2, P)
b = LineBisector(S_1, S_2)
F_2 = Intersect(a, b)
e = Ellipse(F, F_2, P)
f = Hyperbola(F, F_2, P)
g = Parabola(F, Line[S_1, S_2])