https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 3.2.3: Aufgabe 3.5 S. 60
www.kurven-erkunden-und-verstehen.de

Ha 2017

asy

Schnitt

Kurve

m = 1.6 (slider from -5 to 10, step 0.01)
M: (m, 0)
c = 0.8 (slider from -10 to 20, step 0.1)
a = 4 (slider from -5 to 5, step 0.1)
B = (0, 0)
A: (a, 0)
b: y = c
Q = Point(b)
c_1 = Line(B, Q)
d = Circle(Q, A)
P, P' = Intersect(d, c_1)
Ortslinie1 = Locus(P, Q)
Ortslinie2 = Locus(P', Q)
e = Segment(P', Q)
f = Segment(Q, P)
i: (y * (a^(2) - x^(2) - y^(2))) = (c * (((2 * a) * x) - (2 * x^(2)) - (2 * y^(2))))
h: ((x^(2) + y^(2)) * ((2 * c) - y)) = (a * (((2 * c) * x) - (y * a)))
j = false
p(x) = (c^(2) * a^(2)) + (a^(2) * x) - (2 * a^(2)) - x^(4) + ((4 * c) * x^(3)) - ((4 * c^(2)) * x^(2))
C, D, H, I = Root(p)
E, F, G = Extremum(p)
g: y = (2 * c)
k = true
l: (y * (x^(2) + y^(2) - a^(2))) = ((2 * c) * (x^(2) + y^(2) - (a * x)))
J = Intersect(l, g)
n = false
o = false