β

parabole

Additional Constructions

\beta>\alpha ⇒ \;Ellipse

\beta=α ⇒ \;parabole

\beta<\alpha ⇒  \; Hyperbole

angle du plan

position verticale du plan

+

| 

-

 | 

 = 

animer le point

h = 1.6 (slider from 0 to 5, step 0.1)
A = Intersect(xAxis, yAxis)
B = Point(zAxis)
aa = 0.628319
C: (-1, 0, h)
a = Line(C, yAxis)
bb = 0.701 (slider from 0.001 to 1.5707963267948966, step 0.1)
γ: π / 2 - bb
D: (0, 0, (abs(x(C)) * tan(γ)) + h)
b = Plane(D, a)
C' = Mirror(C, D)
c = Ray(D, C')
δ = Angle(c, zAxis)
d = InfiniteCone(A, B, aa)
int = IntersectPath(b, xz)
g = IntersectPath(xz, d)
V2, V1 = Intersect(int, g)
c_1 = Line(A, V1)
c_2 = Line(A, V2)
vert = Line(A, B)
K = Point(c_2)
r = IntersectPath(b, d)
f, i = AngularBisector(c_1, int)
O2 = Intersect(vert, f)
O1 = Intersect(vert, i)
j = OrthogonalLine(O2, c_1, xz)
k = OrthogonalLine(O1, c_1, xz)
G = Intersect(c_1, j)
H = Intersect(c_1, k)
p = Circle(O2, G, xz)
q = Circle(O1, H, xz)
F_1, J = Intersect(int, q)
F_2, M = Intersect(int, p)
l = Sphere(O1, F_1)
m = Sphere(O2, F_2)
tan2 = Circle(zAxis, H)
tan1 = Circle(zAxis, G)
Q = Point(r)
gen = Line(Q, A)
E = Intersect(gen, tan1)
F = Intersect(gen, tan2)
e = Segment(Q, F_2)
n = Segment(Q, F)
s = Segment(Q, F_1)
t = Segment(Q, E)
d_1 = Circle(vert, Q)
o = Plane(tan2)
dir = IntersectPath(o, b)
a_1 = OrthogonalLine(Q, dir, b)
I = Intersect(dir, a_1)
b_1 = OrthogonalLine(Q, a_1, b)
L = Intersect(b_1, int)
N = Intersect(dir, r)
O, P = Intersect(int, r)
R = Intersect(dir, int)
e_1 = Segment(Q, I)
f_1 = Segment(L, R)
S, T = Intersect(b_1, r)
W = PointIn(b)
u = OrthogonalPlane(R, dir)
g_1 = IntersectPath(u, d)
U, V = Intersect(g_1, tan2)
Z, A_1 = Intersect(g_1, d_1)
h_1 = Segment(Z, U)
v = false
par = false
angle = If(bb < aa, text3, If[bb > aa, text1, text2])
text4: "" + (LaTeX[angle]) + ""
text8: "" + s + ""
text10: "" + e + ""
sum: s + e
text11: "   = " + sum + ""
dif: abs(s - e)
text17: "" + e_1 + ""
an = false
text15: " = " + dif + ""
α = Angle(Q, I, R, b)
B_1 = Point(dir)
β = Angle(F_1, R, B_1, b)