雙曲線標準式(2)
Author: 藍邦偉  老師

顯示a²+b²=c²

a=

b=

h=

k=

h

k

b

a

$ 雙曲線標準式(2) $

$ M $

$ A $

A'

$ B $

$ B' $

$ F $

$ F' $

k = 0 (slider from -20 to 20, step 1)
h = 0 (slider from -20 to 20, step 1)
b = 1 (slider from 0 to 6, step 0.5)
a = 1 (slider from 0 to 6, step 0.5)
c: sqrt(a^(2) + b^(2))
Γ: (-(x - h)^(2)) / b^(2) + (y - k)^(2) / a^(2) = 1
d: x = h
e: y = k
M: (h, k)
A: (h, k + a)
B: (h + b, k)
F': (h, k - c)
F: (h, k + c)
K_1: (x(Corner[1]), 0)
K_2: (x(Corner[2]), 0)
K_3: (0, y(Corner[2]))
K_4: (0, y(Corner[3]))
u = Vector(K_1, K_2)
v = Vector(K_3, K_4)
B' = Mirror(B, M)
g = Segment(B, B')
R_1: A + (0, b)
R_2: A - (0, b)
o = false
Step = 0 (slider from 0 to 9, step 1)
T_1 = Corner(1)
T_4 = Corner(4)
T_2: (3.3 * Corner[1] + 1.7 * Corner[2]) / 5
T_3: (3.3 * Corner[4] + 1.7 * Corner[3]) / 5
多邊形2, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
G: (x(Corner[1] + 1) - 0.9, y(0.33 * Corner[1] + 0.67 * Corner[4]))
c_1 = Segment(T_2, T_3)
text6: "中心M(" + h + "," + k + ")"
inputBox1 = Textfield(h)
inputBox2 = Textfield(k)
inputBox3 = Textfield(b)
inputBox4 = Textfield(a)
text7: "貫軸長為" + (LaTeX[2 * a]) + ""
text15: "共軛軸長為 " + (2 * b)
A': (h, k - a)
f = Segment(A, A')
text8: "頂點座標為A(" + (LaTeX[h]) + "," + (LaTeX[k + a]) + "),A'(" + (LaTeX[h]) + "," + (LaTeX[k - a]) + ")"
text12: "正焦弦長為\frac{2b²}{a}=" + (LaTeX[FractionText[2 * b^(2) / a]]) + ""
L = Line(M + (b, a), M)
L' = Line(M + (b, -a), M)
i: y = k + c
j: y = k - c
C, D = Intersect(Γ, i)
E, H = Intersect(Γ, j)
l = Segment(D, C)
m = Segment(H, E)
tri, m_1, a_1, b_1 = Polygon(A, B, M)
text5: "\Gamma：\;\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[b^(2)]) + "}=1"
text13: "$漸近線方程式：$
$" + (LaTeX[L]) + "," + (LaTeX[L']) + "$"
text9: "共軛軸頂點為B(" + (LaTeX[h + b]) + "," + (LaTeX[k]) + "),B'(" + (LaTeX[h - b]) + "," + (LaTeX[k]) + ")"
p = Ray(A, A + (0, 1))
q = Ray(A', A' - (0, 1))
r = PolyLine(A + (b, 0), A' + (b, 0), A' - (b, 0), A - (b, 0), A + (b, 0))
text10_2: "$焦點座標為：$
$F(" + (LaTeX[h]) + "," + (LaTeX[SurdText[k + sqrt(a^(2) + b^(2))]]) + "),F'(" + (LaTeX[h]) + "," + (LaTeX[SurdText[k - sqrt(a^(2) + b^(2))]]) + ")$"