Parábolas

P_4

I

P_3

P_2

P_1

X

Recta de Pascal

$\vec{\mathbf u}$

$\vec{\mathbf v}$

Mostrar la Construcción

o = false
A = (-8.90471091416704, -4.212569199771251)
c = Circle(A, 4)
B = Point(c)
u = Vector(A, B)
P_1 = (4.797475966609562, 2.774196406159535)
P_2 = (2.662281161294155, -1.0958441784746427)
P_3 = (1.0596260176422962, -5.684065963416232)
P_4 = (9.429078722993085, -8.965773920516474)
D = (-3.8041992657280175, 0.7893705648104512)
C = (-5.063895022572128, 0.7893705648104512)
polígono1, i, j, l, m, n, p, E, F, G, H = Polygon(C, D, 6)
a = Line(P_4, u)
M = Point(a)
b = Line(P_1, M)
d = Line(P_3, P_4)
U = Intersect(b, d)
e = Line(P_2, P_1)
V = Intersect(a, e)
f = Line(V, U)
g = Line(P_2, P_3)
W = Intersect(f, g)
h = Line(W, u)
X = Intersect(b, h)
k = Conic(P_1, P_2, P_3, P_4, X)
v, q, w, r = PPPPC_P(P_1, P_2, P_3, P_4)
A' = Translate(A, v)
s = Vector(A, A')
A'_1 = Translate(A, w)
t = Vector(A, A'_1)
a_1 = Ray(A, A')
b_1 = Ray(A, A'_1)
I = Intersect(c, a_1)
u_1 = Vector(A, I)
J = Intersect(c, b_1)
v_1 = Vector(A, J)
c_1 = true

Tool: IPPPP
Conica dada la dirección de un punto del infinto y cuatro puntos más
Input: u, P_1, P_2, P_3, P_4
Output: h, X

a = Line(P_4, u)
M = Point(a)
b = Line(P_1, M)
d = Line(P_1, P_2)
V = Intersect(a, d)
c = Line(P_3, P_4)
U = Intersect(b, c)
e = Line(V, U)
f = Line(P_2, P_3)
W = Intersect(e, f)
g = Line(W, u)
X = Intersect(b, g)
h = Conic(P_1, P_2, P_3, P_4, X)

Tool: PPPPC_P
Parábolas por cuatro puntos
Input: P_1, P_2, P_3, P_4
Output: u, q, v, r

$\Gamma$

$\vec{\mathbf u}$

$\vec{\mathbf v}$

b = Line(P_3, P_4)
c = Line(P_2, P_3)
d = Line(P_1, P_4)
e = Circle(P_1, P_2, P_3)
A = Center(e)
f = Line(P_1, b)
g = OrthogonalLine(A, f)
J = Mirror(P_1, g)
h = Line(P_1, c)
i = OrthogonalLine(A, h)
K = Mirror(P_1, i)
j = OrthogonalLine(A, d)
L = Mirror(P_1, j)
k = Line(K, J)
l = Line(L, P_2)
X = Intersect(l, k)
m = Line(L, J)
n = Line(P_2, K)
Y = Intersect(m, n)
p = Line(X, Y)
N, M = Intersect(e, p)
u = Vector(P_1, M)
v = Vector(P_1, N)
q, B = IPPPP(u, P_1, P_2, P_3, P_4)
r, C = IPPPP(v, P_1, P_2, P_3, P_4)