等軸雙曲線
Author: 藍邦偉  老師

h=

k=

h

k

a=

a

貫軸長=共軛軸長

=正焦弦長

$ 等軸雙曲線 $

a = 1 (slider from -10 to 10, step 1)
h = 0 (slider from -10 to 10, step 1)
k = 0 (slider from -10 to 10, step 1)
L: x - y - h + k = 0
L': x + y - h - k = 0
A: (h + a, k)
Γ: (x - h)^(2) / a^(2) - (y - k)^(2) / a^(2) = 1
A': (h - a, k)
B: (h, k + a)
B': (h, k - a)
b = Segment(A', A)
d = Segment(B, B')
e = Line(B, xAxis)
f = Line(B', xAxis)
g = Line(A', yAxis)
i = Line(A, yAxis)
C = Intersect(g, e)
D = Intersect(i, e)
E = Intersect(f, i)
G = Intersect(f, g)
j = Segment(C, D)
l = Segment(D, E)
m = Segment(E, G)
n = Segment(G, C)
c: 2^(1 / 2) * a
F: (h + c, k)
F': (h - c, k)
p = OrthogonalLine(F, xAxis)
q = OrthogonalLine(F', xAxis)
H, I = Intersect(Γ, q)
J, K = Intersect(Γ, p)
r = Segment(J, K)
s = Segment(H, I)
Γ': (y - k)^(2) / a^(2) - (x - h)^(2) / a^(2) = 1
F_1: (h, k + sqrt(2) * a)
F_2: (h, k - sqrt(2) * a)
t = Line(F_1, xAxis)
a_1 = Line(F_2, xAxis)
M = Intersect(Γ', t, 1)
N = Intersect(Γ', t, 2)
O, P = Intersect(Γ', a_1)
b_1 = Segment(N, M)
c_1 = Segment(P, O)
P_1: (x(Corner[1]), 0)
P_2: (x(Corner[2]), 0)
P_3: (0, y(Corner[2]))
P_4: (0, y(Corner[3]))
u = Vector(P_1, P_2)
v = Vector(P_3, P_4)
T_1 = Corner(1)
T_4 = Corner(4)
T_2: (7.3 * Corner[1] + 2.7 * Corner[2]) / 10
T_3: (7.3 * Corner[4] + 2.7 * Corner[3]) / 10
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
d_1 = Segment(T_2, T_3)
inputBox1 = Textfield(h)
inputBox2 = Textfield(k)
inputBox3 = Textfield(a)
text4_1: "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(k), "y+" * abs(k)]]]) + "" + (LaTeX[If[k ≟ 0, "", ")^2"]]) + "}{" + (LaTeX[a^(2)]) + "}=1"
text5: "Γ':\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)]) + "}-\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)]) + "}=1"