橢圓的參數式
Author: 藍邦偉  老師

移動h,k決定中心
a>b
2a,2b決定
橢圓的長軸與短軸長

橢圓的參數式

k = 1 (slider from -5 to 5, step 1)
h = 1 (slider from -5 to 5, step 1)
a = 4 (slider from 1 to 25, step 1)
b = 3 (slider from 1 to 25, step 1)
M: (h, k)
d = Circle(M, b)
Γ: (x - h)^(2.0) / a^(2.0) + (y - k)^(2.0) / b^(2.0) = 1.0
c = Circle(M, a)
θ = 1.9512781037296605 rad (slider from 0 to 6.283185307179586, step 0.003490658503988659)
P: (h + a * cos(θ), k + b * sin(θ))
e: x = a * cos(θ) + h
D: (h + a * cos(θ), k + a * sin(θ))
g = Segment(M, D)
i: x = b * cos(θ) + h
E = Intersect(i, xAxis)
F = Intersect(e, xAxis)
f: y = b * sin(θ) + k
C: (h + b * cos(θ), k + b * sin(θ))
P_1: M + (a, 0.0)
P_2: M - (a, 0.0)
j = Segment(P_1, P_2)
P_3: M + (0.0, a)
P_4: M - (0.0, a)
l = Segment(P_3, P_4)
Q_1: (x(Corner[1.0]), 0.0)
Q_2: (x(Corner[2.0]), 0.0)
Q_3: (0.0, y(Corner[2.0]))
Q_4: (0.0, y(Corner[4.0]))
u = Vector(Q_1, Q_2)
v = Vector(Q_3, Q_4)
T_4 = Corner(4.0)
T_1 = Corner(1.0)
T_2: (7.0 * Corner[1.0] + 3.0 * Corner[2.0]) / 10.0
T_3: (7.0 * Corner[4.0] + 3.0 * Corner[3.0]) / 10.0
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
m = Segment(T_2, T_3)
文字3: "Γ: \frac{(x" + (If[h < 0.0, "+", "-"]) + (abs(h)) + ")² }{" + (a * a) + " }+ \frac{ (y" + (If[k < 0.0, "+", "-"]) + (abs(k)) + ")² }{ " + (b * b) + "} =1"