2D 座標架
Author: 藍邦偉  老師
Date: 12 1 月 2013

$ O $

$Q_1$

$Q_2$

$A$

$B$

$ 兩圓的根軸方程式 $

$ 座標平面上已知兩圓分別為\;C_1:$
$x^2+y^2+d_1x+e_1y+f_1=0\;與C_2$
$x^2+y^2+d_2x+e_2y+f_2=0，且兩$
$圓交於A,B\;兩點，\;則\overleftrightarrow{AB}方程式為 ：$
$(d_1-d_2)x+(e_1-e_2)y+(f_1-f_2)=0$

$ C_2-C_1得 ：$

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
T_2: 0.67 * Corner[1] + 0.33 * Corner[2]
T_3: (x(T_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], T_2, T_3, Corner[4])
Q_A = (3, 3)
Q_B = (2.76340603868172, 1.779683931631817)
Q_1 = DynamicCoordinates(Q_A, floor(x(Q_A)), floor(y(Q_A)))
Q_2 = DynamicCoordinates(Q_B, floor(x(Q_B)), floor(y(Q_B)))
r_1 = 4 (slider from 1 to 5, step 1)
r_2 = 4 (slider from 1 to 5, step 1)
C_1 = Circle(Q_1, r_1)
C_2 = Circle(Q_2, r_2)
A, B = Intersect(C_2, C_1)
L = Line(A, B)
list1 = Coefficients(C_1)
list2 = Coefficients(C_2)
d_1 = Element(list1, 5)
d_2 = Element(list2, 5)
e_1 = Element(list1, 6)
e_2 = Element(list2, 6)
f_1 = Element(list1, 3)
f_2 = Element(list2, 3)
s = 0 (slider from 0 to 3, step 1)
text1: "$ C_1：\;x^2+y^2" + (LaTeX[If[d_1 ≟ 0, "", If[d_1 > 0, "+" * d_1 * "x", "-" * (-d_1) * "x"]]]) + " " + (LaTeX[If[e_1 ≟ 0, "", If[e_1 > 0, "+" * e_1 * "y", "-" * (-e_1) * "y"]]]) + "" + (LaTeX[If[f_1 ≟ 0, "", If[f_1 > 0, "+" * f_1, "-" * (-f_1)]]]) + "=0$"
text2: "$ C_2：\;x^2+y^2" + (LaTeX[If[d_2 ≟ 0, "", If[d_2 > 0, "+" * d_2 * "x", "-" * (-d_2) * "x"]]]) + " " + (LaTeX[If[e_2 ≟ 0, "", If[e_2 > 0, "+" * e_2 * "y", "-" * (-e_2) * "y"]]]) + "" + (LaTeX[If[f_2 ≟ 0, "", If[f_2 > 0, "+" * f_2, "-" * (-f_2)]]]) + "=0$"
d3: d_2 - d_1
e3: e_2 - e_1
f3: f_2 - f_1
text3_2: "$⇒ " + (LaTeX[If[d3 ≟ 0, "", d3 * "x"]]) + "" + (LaTeX[If[e3 ≟ 0, "", If[e3 > 0, "+" * e3 * "y", "-" * (-e3) * "y"]]]) + " " + (LaTeX[If[f3 ≟ 0, "", If[f3 > 0, "+" * f3, "-" * (-f3)]]]) + "=0$"
g = GCD(abs(d3), GCD[abs(e3), abs(f3)])
r_! = 4
text4_2: "⇒" + (LaTeX[If[d3 ≟ 0, "", If[d3 / g ≟ 1, "x", d3 / g * "x"]]]) + "" + (LaTeX[If[e3 ≟ 0, "", If[e3 / g ≟ 1, "+y", If[e3 / g ≟ -1, "-y", If[e3 > 0, "+" * e3 / g * "y", "-" * (-e3) / g * "y"]]]]]) + "" + (LaTeX[If[f3 ≟ 0, "", If[f3 > 0, "+" * f3 / g, "-" * (-f3) / g]]]) + "=0"
text4_1: "$ ⇒" + (LaTeX[If[d3 ≟ 0, "", -d3 * "x"]]) + " " + (LaTeX[If[e3 ≟ 0, "", If[e3 > 0, "-" * e3 * "y", "+" * (-e3) * "y"]]]) + "" + (LaTeX[If[f3 ≟ 0, "", If[f3 > 0, "-" * f3, "+" * (-f3)]]]) + "=0$"
text5_1: "$ ⇒" + (LaTeX[If[d3 ≟ 0, "", If[d3 / g ≟ -1, "x", (-d3) / g * "x"]]]) + " " + (LaTeX[If[e3 ≟ 0, "", If[e3 / g ≟ 1, "-y", If[e3 / g ≟ -1, "+y", If[e3 > 0, "-" * e3 / g * "y", "+" * (-e3) / g * "y"]]]]]) + "" + (LaTeX[If[f3 ≟ 0, "", If[f3 > 0, "-" * f3 / g, "+" * (-f3) / g]]]) + "=0$"
α = 6.283185307179586 rad (slider from 0 to 6.283185307179586, step 0.1*°)