Parameterkurven für:
Ellipse i=2
Parabel i=0
Hyperbel i=-4

Variiere i mit den 
Pfeiltasten!

https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 7.1: S.180
www.kurven-erkunden-und-verstehen.de

Ha 2016

Kegelschnitte

i = 0 (slider from -5 to 5, step 0.2)
h = 3 (slider from -5 to 20, step 0.1)
b: (h * x) + ((i + 3) * z) = (i * h)
f = IntersectPath(b, xOyPlane)
I: (i, 0, 0)
kegel = Surface((t * cos(th)), (t * sin(th)), t + 3, th, 0, (2 * π), t, -6, 6)
hyp1 = CurveCartesian(t, sqrt((8 * t^(2)) + (54 * t) + 81), (3 * t) + 12, t, -6, 1)
hyp2 = CurveCartesian(t, (-sqrt((8 * t^(2)) + (54 * t) + 81)), (3 * t) + 12, t, -6, 1)
Parabel = CurveCartesian((1 / 6 * t^(2)) - 3 / 2, t, (-1 / 6 * t^(2)) + 3 / 2, t, -8, 8)
H: (-3, 0, h)
normal = Vector(((-h), 0, (-i) - 3))
d: x^(2) + y^(2) = (z - 3)^(2)
elli2 = CurveCartesian(u, ((-sqrt((-16 * u^(2)) + (54 * u) + 81))) / 5, 6 / 5 - (3 / 5 * u), u, -9 / 8, 4.5)
elli1 = CurveCartesian(u, sqrt((-16 * u^(2)) + (54 * u) + 81) / 5, 6 / 5 - (3 / 5 * u), u, -9 / 8, 9 / 2)
S: (0, 0, 3)
g = Line(I, H)
j = Line(S, (3, 0, 0))
e = IntersectPath(b, d)