橢圓的參數式
Author: 藍邦偉  老師

$ 橢圓的參數式 $

P

k = 0 (slider from -3 to 3, step 1)
h = 0 (slider from -3 to 3, step 1)
a = 2 (slider from 1 to 6, step 1)
b = 1 (slider from 1 to 5, step 1)
M: (h, k)
d = Circle(M, b)
Γ: (x - h)^(2) / a^(2) + (y - k)^(2) / b^(2) = 1
c = Circle(M, a)
θ = 0 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)
P_2: M - (a, 0)
j = Segment(P_1, P_2)
P_3: M + (0, a)
P_4: M - (0, a)
l = Segment(P_3, P_4)
Q_1: (x(Corner[1]), 0)
Q_2: (x(Corner[2]), 0)
Q_3: (0, y(Corner[2]))
Q_4: (0, y(Corner[4]))
u = Vector(Q_1, Q_2)
v = Vector(Q_3, Q_4)
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1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
m = Segment(T_2, T_3)
Equation: "$Γ:\frac{" + (LaTeX[If[h ≟ 0, "", "("]]) + "" + (LaTeX[If[h ≟ 0, "x^2", If[h > 0, "x-" * abs(h), "x+" * abs(h)]]]) + "" + (LaTeX[If[h ≟ 0, "", ")^2"]]) + "}{" + (LaTeX[a^(2)]) + "}+\frac{" + (LaTeX[If[k ≟ 0, "", "("]]) + "" + (LaTeX[If[k ≟ 0, "y^2", If[k > 0, "y-" * abs(h), "y+" * abs(k)]]]) + "" + (LaTeX[If[k ≟ 0, "", ")^2"]]) + "}{" + (LaTeX[b^(2)]) + "}=1$
$\left\lbrace \begin{array}{ll} x=" + (LaTeX[If[h ≟ 0, "", h * "+"]]) + " " + (LaTeX[a]) + "cosθ\\ y=" + (LaTeX[If[k ≟ 0, "", k * "+"]]) + "  " + (LaTeX[If[b ≟ 1, "", b]]) + "sinθ\end{array}  \right.\;,0≤θ<2π$"