View Geometric Solution

$Archimedes\;assumes\;\overline{IJ}\;is\;Minor\;Axis$

$Apollonius\;assumes\;\overline{IJ}\;is\;Major\;Axis$

03-13-2014

M = 2.3 (slider from 0 to 5, step 0.1)
m = 1.8 (slider from 0 to M, step 0.1)
O = (-8.91, 5.22)
Ox: x(O)
Oy: y(O)
c: ((x - Ox) / m)^(2) + ((y - Oy) / M)^(2) = 1
a = Line(O, xAxis)
b = Line(O, yAxis)
A = Intersect(c, b, 2)
B = Intersect(c, a, 1)
distanceOB = Distance(O, B)
TextOB: "\overline{" + (Name[O]) + "" + (Name[B]) + "} \, = \, " + (LaTeX[distanceOB]) + ""
distanceOA = Distance(O, A)
TextOA: "\overline{" + (Name[O]) + "" + (Name[A]) + "} \, = \, " + (LaTeX[distanceOA]) + ""
d = Segment(O, A)
e = Segment(O, B)
C_1 = (3.945616699104015, 4.343171691819263)
f = Circle(C_1, 5)
D = Point(f)
g = Line(C_1, D)
E = Intersect(f, g, 2)
G = Point(g)
h = OrthogonalLine(G, g)
I, J = Intersect(f, h)
OA = Distance(O, A)
OB = Distance(O, B)
pl: OB^(2) / OA
p: pl / OA
k = Circle(I, (p * Distance[I, J]))
P = Intersect(k, h, 2)
i = Ray(E, I)
j = Ray(E, J)
l = Segment(E, D)
n = Line(P, j)
Q = Intersect(n, i)
r = Line(Q, h)
q = Segment(P, Q)
L = Intersect(f, r, 1)
a_1 = Segment(L, E)
C = Point(h)
s = Line(E, C)
t = Line(G, s)
K = Intersect(f, s, 2)
f_1 = Line(G, s)
c_1 = Ray(K, J)
d_1 = Ray(K, D)
e_1 = Ray(K, I)
g_1 = OrthogonalLine(G, d_1)
S = Point(h)
i_1 = Line(S, s)
T = Intersect(j, i_1)
U = Intersect(i, i_1)
F = Intersect(i_1, c_1)
H = Intersect(i_1, e_1)
poly1, u, e_2, t_1 = Polygon(E, T, U)
poly2, h_1, k_1, f_2 = Polygon(K, F, H)
o = false
b_1 = Line(K, h)
N = Intersect(i_1, b_1)
j_1 = Line(E, h)
R = Intersect(i_1, j_1)
l_1 = Segment(E, R)
m_1 = Segment(K, N)
text4: "$\frac{\overline{IP}}{\overline{IJ}}=\frac{\overline{OB}^2}{\overline{OA}^2}=" + (LaTeX[Distance[I, P] / Distance[I, J]]) + " $"
text5: "$\frac{\overline{OB}^2}{\overline{OA}^2}= " + (LaTeX[OB^(2) / OA^(2)]) + "$"
text1: "$\frac{\overline{OB}}{\overline{OA}}=\frac{\overline{m}}{\overline{M}}=\frac{" + (LaTeX[m]) + "}{" + (LaTeX[M]) + "}=" + (LaTeX[OB / OA]) + "$"
text7: "$\frac{\overline{OB}^2}{\overline{OA}^2}= " + (LaTeX[OB^(2) / OA^(2)]) + " $"
text8: "$\frac{\overline{HN}*\overline{FN}}{\overline{KN}^2}=" + (LaTeX[(Distance[H, N] * Distance[F, N] / Distance[K, N]^(2))]) + " $"
text3: "$\frac{\overline{FS}*\overline{SH}}{\overline{IS}*\overline{SJ}}=" + (LaTeX[(Distance[F, S] * Distance[S, H] / ((Distance[I, S] * Distance[S, J])))]) + "$"
text10: "$\frac{\overline{OA}^2}{\overline{OB}^2}=  " + (LaTeX[Distance[A, O]^(2) / OB^(2)]) + " $"
text11: "$\frac{\overline{UR}*\overline{TR}}{\overline{ER}^2}= " + (LaTeX[(Distance[U, R] * Distance[T, R] / Distance[E, R]^(2))]) + " $"
text2: "$\frac{\overline{TS}*\overline{SU}}{\overline{IS}*\overline{SJ}}=" + (LaTeX[(Distance[T, S] * Distance[S, U] / ((Distance[I, S] * Distance[S, J])))]) + "$"