雙曲線標準式(1)
Author: 藍邦偉  老師

顯示a²+b²=c²

a=

b=

h=

k=

雙曲線方程式

漸近線方程式:

h

k

b

a

Reset

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) / a^(2) - (y - k)^(2) / b^(2) = 1
d: x = h
e: y = k
M: (h, k)
A_1: (h + a, k)
A', A = Intersect(Γ, e)
B: (h, k + b)
f = Line(A', A)
F': (h - c, k)
F: (h + c, k)
i = OrthogonalLine(F, f)
j = OrthogonalLine(F', f)
A_3, C = Intersect(Γ, i)
D, E = Intersect(Γ, j)
m = Segment(E, D)
多邊形1, p, q, r = Polygon(B, M, A)
l = Segment(C, A_3)
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')
n_1 = Segment(A, A')
R_1: A + (0, b)
R_2: A - (0, b)
R_3: A' + (0, b)
R_4: A' - (0, b)
s = Segment(R_1, R_2)
t = Segment(R_3, R_4)
a_1 = Segment(R_3, R_1)
b_1 = Segment(R_2, R_4)
L = Line(R_1, R_4)
L' = Line(R_3, R_2)
o = false
n = 0 (slider from 0 to 9, step 1)
T_1 = Corner(1)
T_4 = Corner(4)
T_2: (3.1 * Corner[1] + 1.9 * Corner[2]) / 5
T_3: (3.1 * Corner[4] + 1.9 * Corner[3]) / 5
多邊形2, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
c_1 = Segment(T_2, T_3)
G: (x(Corner[1] + 1), y(0.33 * Corner[1] + 0.67 * Corner[4]))
text5: "\frac{(x" + (If[h > 0, "-", "+"]) + (abs(h)) + ")²}{" + (a^(2)) + "}-\frac{(y" + (If[k > 0, "-", "+"]) + (abs(k)) + ")²}{" + (b^(2)) + "}=1"
text6: "中心M(" + h + "," + k + ")"
text8: "頂點座標為A(" + (h + a) + "," + k + "),A'(" + (h - a) + "," + k + ")"
text9: "貫軸頂點座標為B(" + h + "," + (k + b) + "),B'(" + h + "," + (k - b) + ")"
sq: s * q
text10: "焦點座標為F(" + h + "+\sqrt{" + (a^(2) + b^(2)) + "}," + k + ")"
text11: "與F'(" + h + "-\sqrt{" + (a^(2) + b^(2)) + "}," + k + ")"
text14: "" + (LaTeX[L]) + "," + (LaTeX[L']) + ""
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)
text12: "正焦弦長為\frac{2b²}{a}=" + (LaTeX[FractionText[2 * b^(2) / a]]) + ""