橢圓的標準式(2)
Author: 藍邦偉  老師

a²=b²+c²

k = 8 (slider from -20 to 20, step 1)
h = 5 (slider from -20 to 20, step 1)
b = 3 (slider from 0 to 36, step 0.5)
a = 6 (slider from 0 to 36, step 1)
c: sqrt(a^(2.0) - b^(2.0))
Γ: (x - h)^(2.0) / b^(2.0) + (y - k)^(2.0) / a^(2.0) = 1.0
d: x = h
e: y = k
M: (h, k)
A: (h, k + a)
B: (h + b, k)
F: (h, k + c)
多邊形1, f_1, b_1, m_1 = Polygon(B, M, F)
文字2: "中心為M(" + h + "," + k + ")"
文字4: "短軸的長度為" + (2.0 * b)
K_1: (x(Corner[1.0]), 0.0)
K_2: (x(Corner[2.0]), 0.0)
K_3: (0.0, y(Corner[2.0]))
K_4: (0.0, y(Corner[3.0]))
u = Vector(K_1, K_2)
v = Vector(K_3, K_4)
A': (h, k - a)
F': (h, k - c)
B': (h - b, k)
f = Segment(A, A')
g = Segment(B, B')
i = OrthogonalLine(F, v)
j = OrthogonalLine(F', v)
C = Intersect(Γ, i, 2.0)
D = Intersect(Γ, i, 1.0)
E = Intersect(Γ, j, 2.0)
G = Intersect(Γ, j, 1.0)
l = Segment(C, D)
m = Segment(E, G)
n = 7 (slider from 0 to 7, step 1)
T_1 = Corner(1.0)
T_4 = Corner(4.0)
o = false
T_2: (12.0 * Corner[1.0] + 7.0 * Corner[2.0]) / 19.0
T_3: (12.0 * Corner[4.0] + 7.0 * Corner[3.0]) / 19.0
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)
文字8: "正焦弦長為 \frac{ 2b² }{a }= \frac{ 2(" + (b^(2.0)) + ") }{" + a + " }  =  " + (2.0 * b^(2.0) / a)
文字6: "短軸端點的座標是B(" + (h + b) + "," + k + "),B'(" + (h - b) + "," + k + ")"
文字3: "長軸的長度為" + (2.0 * a)
文字5: "長軸頂點的座標是A(" + h + "," + (k + a) + "),A'(" + h + "," + (k - a) + ")"
文字1: "橢圓方程式Γ: \frac{(x" + (If[h > 0.0, "-", "+"]) + (abs(h)) + ")² }{" + (b * b) + " }+ \frac{ (y" + (If[k > 0.0, "-", "+"]) + (abs(k)) + ")² }{ " + (a * a) + "} =1"
文字7: "焦點F(" + h + "," + k + "+ \sqrt{" + (a^(2.0) - b^(2.0)) + "  } ),F'(" + h + "," + k + "- \sqrt{ " + (a^(2.0) - b^(2.0)) + " } )"