θ

t

Polar-Funktion für Ellipse

Ellipse erkunden

1 Segment ☛ 1 Monat

eps = 0.6 (slider from -5 to 5, step 0.1)
O = Intersect(xAxis, yAxis)
p = 1 (slider from -5 to 5)
r(x) = p / (1 - (eps * cos(x)))
P_0: (r(0), 0)
P_1: (r(0.16); 0.16)
K = Point(r)
A: (x(K), 0)
θ: x(K)
P: (r(θ); θ)
f: y = 1
a(x) = 1 / 2 / ((((-3)) / 5 * cos(x)) + 1)^(2)
Ortslinie1 = Locus(P, K)
P_3: (r(π); π)
B = Point(Ortslinie1)
C = Point(Ortslinie1)
D = Point(Ortslinie1)
E = Point(Ortslinie1)
F = Point(Ortslinie1)
G = Point(Ortslinie1)
H = Point(Ortslinie1)
v1, i, k, l = Polygon(O, P_0, P_1)
J = Point(Ortslinie1)
G_2: (π / 2, 0)
G_3: (π, 0)
Q = Point(a)
Q_x: (x(Q), 0)
t = Integral(a, 0, x(Q))
T: (x(Q), t)
a_0: a(0)
gl1: x = π
T_W = 3.07 (slider from -5 to 5, step 0.01)
l1 = Sequence(0, T_W, T_W / 6)
l2 = Sequence(y = Element[l1, i], i, 1, 7)
R = Point(l2)
U = Point(l2)
V = Point(l2)
W = Point(l2)
Z = Point(gl1)
Vp: (r(0.35); 0.35)
Up: (r(0.6); 0.6)
Sp: (r(0.87); 0.87)
S: (0.87, 2.05)
Rp: (r(1.46); 1.46)
Wp: (r(0.16); 0.16)
Rp' = Mirror(Rp, xAxis)
Sp' = Mirror(Sp, xAxis)
Up' = Mirror(Up, xAxis)
Vp' = Mirror(Vp, xAxis)
Wp' = Mirror(Wp, xAxis)
g_1 = Segment(O, Sp)
h_1 = Segment(O, Up)
i_1 = Segment(O, Vp)
j_1 = Segment(O, Rp')
k_1 = Segment(O, Sp')
m_1 = Segment(O, Up')
n_1 = Segment(O, Vp')
p_1 = Segment(O, Wp')
Ortslinie2 = Locus(T, Q)
Vieleck1, p_3, o, rp, j, h, g, f_1, e, d, c_1 = Polygon(P_3, O, Rp, J, H, G, F, E, D, C)
b = false
Text2: "r=r(x)=" + (LaTeX[r]) + ""
I = (-0.8334485210672353, 1.016518991827418)
L = (-0.20533048364594264, 1.016518991827418)