雙曲線的參數式
Author: 藍邦偉  老師

a>b

雙曲線的參數式

\left\{\begin{array} x=h+ asecθ }  \ y=k+b tanθ  \ \end{array}\right ,0≤θ<2π

θ = 3.6407568196601714 rad (slider from 0 to 6.283185307179586, step 0.003490658503988659)
k = 0 (slider from -5 to 5, step 1)
h = 0 (slider from -5 to 5, step 1)
b = 2 (slider from 1 to 10, step 1)
m: x = h + b
i: y = k + b * tan(θ)
a = 3 (slider from 1 to 10, step 1)
M: (h, k)
d = Circle(M, a)
e = Circle(M, b)
f: x = h
g: y = k
A, R = Intersect(e, g)
D = Intersect(d, f, 2.0)
P: (h + a / cos(θ), k + b * tan(θ))
j: x = h + a / cos(θ)
Q = Intersect(g, j)
L_1: y - k = tan(θ) * (x - k)
S: (h + a * cos(θ), k + a * sin(θ))
l = OrthogonalLine(S, L_1)
T = Intersect(i, m)
p = Ray(R, T)
q = Segment(R, T)
r = Segment(P, Q)
s = Segment(M, Q)
c = CurveCartesian(h + a / cos(φ), k + b * tan(φ), φ, 0.0, 6.28319)
K = (11, 0)
K' = Rotate(K, θ, M)
α = Angle(K, M, K')
n = Line(M, T)
P_1: (x(Corner[1.0]), 0.0)
P_2: (x(Corner[2.0]), 0.0)
P_3: (0.0, y(Corner[1.0]))
P_4: (0.0, y(Corner[4.0]))
u = Vector(P_1, P_2)
v = Vector(P_3, P_4)
T_1 = Corner(1.0)
T_4 = Corner(4.0)
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)
t = Segment(T_2, T_3)
文字3: "\left\{\begin{array} x=" + h + (If[cos(θ) < 0.0, "-", "+"]) + " \frac{" + (abs(a)) + "}{" + (abs(cos(θ))) + " }   \\y=" + k + (If[tan(θ) < 0.0, "-", "+"]) + (abs(b)) + (abs(tan(θ))) + " \\ \end{array}\right"