橢圓的方程式(2)
Author: 藍邦偉  老師
Date: 8 12 月 2012

a²=b²+c²

h=

k=

a=

b=

a

b

h

k

a>b,a²=b²+c²

$ 橢圓方程式(2) $

$ M $

$ A $

$ A' $

$ B $

$ B' $

$ F $

$ F' $

k = 0 (slider from -20 to 20, step 1)
h = 0 (slider from -20 to 20, step 1)
b = 1 (slider from 0 to 10, step 1)
a = 2 (slider from 0 to 10, step 1)
c: sqrt(a^(2) - b^(2))
Γ: (x - h)^(2) / b^(2) + (y - k)^(2) / a^(2) = 1
d: x = h
e: y = k
M: (h, k)
A: (h, k + a)
B: (h + b, k)
F': (h, k - c)
F: (h, k + c)
多邊形1, f_1, b_1, m_1 = Polygon(B, M, F)
K_1: (x(Corner[1]), 0)
K_2: (x(Corner[2]), 0)
K_3: (0, y(Corner[2]))
K_4: (0, y(Corner[3]))
u = Vector(K_1, K_2)
v = Vector(K_3, K_4)
Step = 0 (slider from 0 to 7, step 1)
o = false
T_4 = Corner(4)
T_1 = Corner(1)
T_2: (7 * Corner[1] + 3 * Corner[2]) / 10
T_3: (7 * Corner[4] + 3 * Corner[3]) / 10
多邊形2, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
p = Segment(T_2, T_3)
A': (h, k - a)
f = Segment(A', A)
i = OrthogonalLine(F', u)
j = OrthogonalLine(F, u)
C, D = Intersect(Γ, i)
E, G = Intersect(Γ, j)
H: (19 / 20 * x(Corner[1] + 1 / 20 * x(Corner[2])) - 0.85, 2 / 5 * y(Corner[1]) + 3 / 5 * y(Corner[4]))
A_a = Textfield(a)
B_b = Textfield(b)
H_h = Textfield(h)
K_k = Textfield(k)
text6: "中心M(" + h + "," + k + ")"
text7: "長軸長為" + (2 * a) + "," + "短軸長為" + (2 * b)
text12: "正焦弦長\frac{2b²}{a}=" + (FractionText[2 * b^(2) / a])
text8: "長軸頂點A(" + (LaTeX[h]) + "," + (LaTeX[k + a]) + "),A'(" + (LaTeX[h]) + "," + (LaTeX[k - a]) + ")"
text9: "短軸頂點B(" + (LaTeX[h + b]) + "," + (LaTeX[k]) + "),B'(" + (LaTeX[h - b]) + "," + (LaTeX[k]) + ")"
B': (h - b, k)
t_f: "$\Gamma：\; \frac{" + (LaTeX[If[h ≟ 0, "", "("]]) + "" + (LaTeX[If[h ≟ 0, "x^2", If[h > 0, "x-" * abs(h), "x+" * abs(h)]]]) + "" + (LaTeX[If[h ≟ 0, "", ")^2"]]) + "}{" + (LaTeX[b^(2)]) + "} +\frac{" + (LaTeX[If[k ≟ 0, "", "("]]) + "" + (LaTeX[If[k ≟ 0, "y^2", If[k > 0, "y-" * abs(k), "y+" * abs(k)]]]) + "" + (LaTeX[If[k ≟ 0, "", ")^2"]]) + "}{" + (LaTeX[a^(2)]) + "}=1$"
g = Segment(B, B')
q = Line(F, u)
I, J = Intersect(Γ, q)
r = Line(F', y = y(F'))
K, L = Intersect(Γ, r)
l = Segment(J, I)
m = Segment(K, L)
text10: "焦點F\;(" + (LaTeX[h]) + "," + (LaTeX[SurdText[k + sqrt(a^(2) - b^(2))]]) + ")"
text11: "焦點F'(" + (LaTeX[h]) + "," + (LaTeX[SurdText[k - sqrt(a^(2) - b^(2))]]) + ")"