X

|EX| + |FX| = 2a

q

p

1) Vzhledem k symetrii je |AE| = |BF|

2) Pro bod A platí |AE| + |AF| = 2a,
    kde a je to záhadné číslo z definice.

3) Proto |AB| = rovněž 2a!

4) Proto |AS| = |BS| = a

5) |AS| = |BS| = a → hlavní poloosa

6) Označme |CS| = |DS| = b → vedlejší poloosa

7) Pro bod C platí |CE| + |CF| = 2a. 
    Ale ∆EFC je rovnoramenný →  |CE| = |CF| = a!

8) Označme |ES| = |FS| = e → excentricita

9) ∆CSF → charakteristický trojúhelník elipsy

a 

b

e

e² = a² - b²

a = 2
E: ((-a), 0)
B_1: (a, 0)
b = Segment(E, B_1)
F = Point(b)
e = Circle(F, a)
H = (-1.6686051001090474, -4.660094519847377)
I = (4.238890176469009, -4.672992981149949)
c = LineBisector(E, F)
C_1 = Intersect(e, c, 2)
d = Ellipse(E, F, C_1)
X = Point(d)
f = Segment(E, X)
g = Segment(F, X)
h = Segment(F, E)
Q: X
i = Line(E, F)
A_1 = Point(i)
D_1 = Point(i)
j = Segment(A_1, D_1)
n = LineBisector(E, F)
S = Intersect(n, j)
G = Point(n)
J = Point(n)
p = Segment(G, J)
t = Ellipse(E, F, X)
C, D = Intersect(t, p)
A, B = Intersect(t, j)
k = Segment(E, A)
l = Segment(F, B)
K: A + (0, 0.05)
L: F + (0, 0.05)
m = Segment(K, L)
q = Segment(A, S)
o = ConstructionStep()
r = Segment(S, C)
s = Segment(E, C)
d_1 = Segment(C, F)
a_1 = Segment(C, F)
u = ConstructionStep()
b_1 = Segment(S, F)
mnohoúhelník1, c_1, s_1, f_1 = Polygon(S, F, C)