拋物線的定義(2)
Author: 藍邦偉  老師
Date: 9 12 月 2012

焦點F(

x_0

y_0

,

)

L:y=

準線方程式

L:x=

開口左右

開口上下

對稱軸方程式

頂點座標

Start 1

拋物線的定義

Start2

t_1 = 0 (slider from -2 to 2, step 0.01)
h_1 = 1 (slider from -6 to 6, step 1)
L_1: x = h_1
y_0 = 0 (slider from -5 to 5, step 0.1)
x_0 = 0 (slider from -6 to 6, step 0.1)
F: (x_0, y_0)
L_3: y = y(F)
A_1 = Intersect(L_1, L_3)
V_1 = Midpoint(F, A_1)
O = (0, 0)
c_1: x(F) - x(V_1)
A_5 = Corner(1)
A_4 = Corner(4)
A_3: 0.3 * Corner[3] + 0.7 * A_4
A_6: 0.3 * Corner[2] + 0.7 * A_5
Poly1, a_1, a_2, a_3, a_4 = Polygon(A_5, A_6, A_3, A_4)
g = Segment(A_6, A_3)
inputBox1 = Textfield(x_0)
inputBox2 = Textfield(y_0)
k_1 = 1 (slider from -5 to 5, step 1)
L_2: y = k_1
k = Textfield(k_1)
h = Textfield(h_1)
F_1: (y - y(V_1))^(2) = 4 * (x(F) - x(V_1)) * (x - x(V_1))
P_1: (x(V_1) + c_1 * t_1^(2), y(V_1) + 2 * c_1 * t_1)
C_1 = Circle(P_1, F)
Q_1: (h_1, y(P_1))
d = Segment(P_1, Q_1)
e = Segment(F, P_1)
L_U: y = y(Corner[3])
L_D: y = y(Corner[1])
UB, B = Intersect(F_1, L_U)
LB, C = Intersect(F_1, L_D)
n = 0 (slider from 0 to 1, step 1)
A = (-10.02, 2.5)
L_4: y = k_1
text12: "l:x=" + (x(F))
text14: "V(" + (LaTeX[x_0 - c_1]) + "," + (LaTeX[y_0]) + ")"
l_1: y = y(F)
l_2: x = x(F)
A_2 = Intersect(L_4, l_2)
V_2 = Midpoint(F, A_2)
c_2: y(F) - y(V_2)
F_2: (x - x(V_2))^(2) = 4 * c_2 * (y - y(V_2))
text15: "V(" + (x(F)) + "," + (y(F) - c_2) + ")"
t_2 = 0 (slider from -2 to 2, step 0.01)
P_2: (x(V_2) + 2 * c_2 * t_2, y(V_2) + c_2 * t_2^(2))
C_2 = Circle(P_2, F)
a = Segment(F, P_2)
Q_2: (x(P_2), k_1)
b = Segment(P_2, Q_2)
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
text7: "l:y=" + (y(F))
D = (-10.96, 4.26)
text16: "$ \Gamma：\;" + (LaTeX[If[x(V_2) ≟ 0, "x", "(x"]]) + " " + (LaTeX[If[x(V_2) ≟ 0, "", If[x(V_2) > 0, "-" * abs(x(V_2)), "+" * abs(x(V_2))]]]) + "" + (LaTeX[If[x(V_2) ≟ 0, "^2", ")^2"]]) + "=" + (LaTeX[4 * c_2]) + "" + (LaTeX[If[y(V_2) ≠ 0, "(", ""]]) + "y" + (LaTeX[If[y(V_2) ≟ 0, "", If[y_0 > 0, "-" * abs(y(V_2)), "+" * abs(y(V_2))]]]) + "" + (LaTeX[If[y(V_2) ≠ 0, ")", ""]]) + "$"
text6_1: "$ \Gamma：\; " + (LaTeX[If[y(V_1) ≟ 0, "", "("]]) + "y" + (LaTeX[If[y(V_1) > 0, "-" * abs(y(V_1)), If[y(V_1) ≟ 0, "", "+" * abs(y(V_1))]]]) + "" + (LaTeX[If[y(V_1) ≟ 0, "^2", ")^2"]]) + "=" + (LaTeX[4 * c_1]) + "" + (LaTeX[If[x(V_1) ≟ 0, "", "("]]) + "x" + (LaTeX[If[x(V_1) > 0, "-" * abs(x(V_1)), If[x(V_1) < 0, "+" * abs(x(V_1)), ""]]]) + "" + (LaTeX[If[x(V_1) ≟ 0, "", ")"]]) + "$"