過雙曲線上一點的切線與兩漸近線所圍的三角形面積
Author: 藍邦偉  老師

過雙曲線上一點的切線

與兩漸近線所圍之三角形面積

a=

b=

h=

k=

h

k

a

b

θ = 0 rad (slider from 0 to 6.283185307179586, step 0.0017453292519943296)
k = 10 (slider from -20 to 20, step 1)
h = 7 (slider from -20 to 20, step 1)
b = 7 (slider from 0 to 20, step 1)
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')
T_1 = Corner(1)
T_4 = Corner(4)
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)
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)
i, j = Tangent(P, c)
A = Intersect(L, i)
B = Intersect(i, L')
TA, c_1, a_1, b_1 = Polygon(A, B, C)
text7: "\frac{(x" + (If[h > 0, "-", "+"]) + (abs(h)) + ")²}{" + (a^(2)) + "}-\frac{(y" + (If[k > 0, "-", "+"]) + (abs(k)) + ")²)}{" + (b^(2)) + "}=1"
text8: "ΔABC的面積是" + TA
inputBox1 = Textfield(h)
inputBox2 = Textfield(k)
inputBox3 = Textfield(a)
inputBox4 = Textfield(b)