雙曲線上一點到兩漸近線距離為定值
Author: 藍邦偉  老師

雙曲線上一點到兩

漸近線乘積為定值

a=

b=

h=

k=

a

b

h

k

θ = 0 rad (slider from 0 to 6.283185307179586, step 0.01*°)
k = 0 (slider from -20 to 20, step 1)
h = 0 (slider from -20 to 20, step 1)
b = 15 (slider from 0 to 20, step 0.5)
a = 10 (slider from 0 to 20, step 1)
c: (x - h)^(2) / a^(2) - (y - k)^(2) / b^(2) = 1
e: x = h + a
f: x = h - a
L: b * (x - h) - a * (y - k) = 0
L': b * (x - h) + a * (y - k) = 0
C = Intersect(L, L')
P: (h + a / cos(θ), k + b * tan(θ))
d = OrthogonalLine(P, L)
g = OrthogonalLine(P, L')
H = Intersect(d, L)
H' = Intersect(g, L')
i = Segment(P, H)
j = Segment(P, H')
T_1 = Corner(1)
T_4 = Corner(4)
T_3: (7.3 * Corner[4] + 2.7 * Corner[3]) / 10
T_2: (7.3 * Corner[1] + 2.7 * Corner[2]) / 10
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
l = Segment(T_2, T_3)
A_1: (x(Corner[1]), 0)
A_2: (x(Corner[2]), 0)
A_3: (0, y(Corner[2]))
A_4: (0, y(Corner[3]))
u = Vector(A_1, A_2)
v = Vector(A_3, A_4)
text3: "\frac{(x" + (If[h > 0, "-", "+"]) + (abs(h)) + ")²}{" + (a^(2)) + "}-\frac{(y" + (If[k > 0, "-", "+"]) + (abs(k)) + ")²}{" + (b^(2)) + "}=1"
ij: i * j
inputBox1 = Textfield(a)
inputBox2 = Textfield(b)
inputBox3 = Textfield(h)
inputBox4 = Textfield(k)
text5: "\overline{PH}×\overline{PH'}=" + i + "×" + j
text4: "=" + (LaTeX[ij]) + "=\frac{" + (LaTeX[a^(2)]) + "×" + (LaTeX[b^(2)]) + "}{" + (LaTeX[a^(2)]) + "+" + (LaTeX[b^(2)]) + "}"