Parabel mit Bärenkasten
Author: Prof. dr. Dörte Haftendorn
Date: (96) Feb 05

Parabel mit Bärenkasten

Ha 05

Brennpunkt usw

Scherung

p(x) = 0.25 * x^(2.0)
A = Point(p)
B = Point(p)
a = Segment(A, B)
b = LineBisector(A, B)
M = Intersect(a, b)
c = OrthogonalLine(M, xAxis)
C = Intersect(p, c)
d = Tangent(C, p)
e = OrthogonalLine(A, xAxis)
f = OrthogonalLine(B, xAxis)
D = Intersect(e, d)
E = Intersect(f, d)
F = Midpoint(D, C)
G = Midpoint(D, A)
H = Midpoint(D, G)
J = Midpoint(C, E)
h = Line(G, d)
i = Line(H, d)
j = Line(F, yAxis)
k = Line(J, yAxis)
P, d_1, e_1, b_1, a_1 = Polygon(D, E, B, A)
Q = Intersect(h, f)
R = Intersect(i, f)
T = Intersect(j, a)
V = Intersect(k, a)
q = Segment(T, F)
r = Segment(M, C)
s = Segment(V, J)
c_1 = Segment(G, Q)
f_1 = Segment(H, R)
I = Intersect(s, d)
K = Intersect(q, d)
g = Line(B, I)
m = Line(A, K)
l = Line(A, B)
L = Intersect(a_1, c_1)
n: y(B) - y(A)
g_1(x) = (y(B) - y(A)) / (x(B) - x(A)) * (x - x(A)) + y(A)
flaeche = Integral(g_1, p, x(A), x(B))
N = Midpoint(L, A)
t = Line(N, d)
O = Intersect(t, e_1)
h_1 = Segment(N, O)
S = Focus(k_1)
U = Intersect(g, xAxis)
S' = Mirror(S, U)
o = false
u = Slope(d)
df(x) = u * (x - x(C)) + y(C)
p_1(x) = p(x) - df(x)
v = false