94學測雙曲線一題
Author: 藍邦偉  老師

x

y

94學測雙曲線一題

Γ: \frac{x²}{9 }- \frac{y² }{16 }=1

P

P

第一個三角形

第二個三角形

a²=9,b²=16=>a=3,b=4,c=5

| \overline{ PF_1 }- \overline{ PF_2 }|=6  

 \overline{ PF_1 }= \overline{ F_1F_2 }=10  

 \overline{ PF_2 }=4,16 

 \overline{ PF_1 }= \overline{ F_1F_2 }=10  

 \overline{ PF_1 }+ \overline{ PF_2 }+ \overline{ F_1F_2 }=24,36   

k = -2.4 (slider from -5 to 5, step 0.1)
A_0 = Corner(1.0)
B_0 = Corner(3.0)
C_0: (x(A_0), 0.0)
D_0: (x(B_0), 0.0)
u = Vector(C_0, D_0)
E_0: (0.0, y(A_0))
F_0: (0.0, y(B_0))
v = Vector(E_0, F_0)
A = Point(u)
B = (0, 0)
O = (0, 0)
g: x = k
F_1 = (5, 0.15337763733967513)
F_2 = (-5, 0.15337763733967513)
c = Circle(F_1, 10.0)
C, D, E, F = Intersect(d, c)
多邊形1, f_2, e, f_1 = Polygon(E, F_1, F_2)
多邊形2, f_3, f, f_4 = Polygon(F, F_1, F_2)
a = false
b = false
T_1 = Corner(1.0)
T_4 = Corner(4.0)
T_2: (7.0 * Corner[1.0] + 3.0 * Corner[2.0]) / 10.0
T_3: (7.0 * Corner[4.0] + 3.0 * Corner[3.0]) / 10.0
多邊形3, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
n = 2 (slider from 0 to 6, step 1)