圓的一般式
Author: 藍邦偉　老師
Date: 9 1 月 2013

圓的一般式

$Q$

d

e

f

d=

$ e= $

f=

$ 圓的一般式 $

$Step=%v$

$C：\; x^2+y^2+dx+ey+f=0 $
$\;\;\;\;\;\;\Delta =d^2+e^2-4f>0$

$ 你的輸入沒有滿足$
$\Delta =d^2+e^2-4f>0 $

公式法

配方法

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
d = 0 (slider from -8 to 8, step 1)
e = 6 (slider from -8 to 8, step 1)
f = -5 (slider from -10 to 10, step 1)
C_1: x^(2) + y^(2) + d * x + e * y + f = 0
Q_1 = Corner(1)
Q_4 = Corner(4)
Q_2: (6 * Corner[1] + 4 * Corner[2]) / 10
Q_3: (6 * Corner[4] + 4 * Corner[3]) / 10
多邊形1, t_1, t_2, t_3, t_4 = Polygon(Q_1, Q_2, Q_3, Q_4)
Q: ((-d) / 2, (-e) / 2)
a = Segment(Q_2, Q_3)
inputBox1 = Textfield(d)
inputBox2 = Textfield(e)
inputBox3 = Textfield(f)
s = 0 (slider from 0 to 8, step 1)
D: d^(2) + e^(2) - 4 * f
text6: "圓心是\;Q(-\frac{d}{2},-\frac{e}{2})⇒Q(\;" + (LaTeX[FractionText[x(Q)]]) + "\;,\;" + (LaTeX[FractionText[y(Q)]]) + "\;)"
text7: "$半徑\;r=\frac{1}{2}\sqrt{d^2+e^2-4f}$
$\;\;\;\;\;\;\;\;\;\;\;=\frac{1}{2}\sqrt{" + (LaTeX[d^(2)]) + "+" + (LaTeX[e^(2)]) + "" + (LaTeX[If[f > 0, "-", "+"]]) + "" + (LaTeX[abs(4 * f)]) + "}$"
text5: "⇒Q" + (LaTeX[FractionText[Q]]) + ",r=" + (LaTeX[SurdText[sqrt(d^(2) + e^(2) - 4 * f) / 2]]) + ""
text8: "=\frac{1}{2}\sqrt{" + (LaTeX[d^(2) + e^(2) - 4 * f]) + "}=" + (LaTeX[SurdText[sqrt(d^(2) + e^(2) - 4 * f) / 2]]) + ""
text1: "x²+y²" + (LaTeX[If[d > 0, "+" + d + "x", If[d < 0, "-" + (abs(d)) + "x", ""]]]) + "" + (LaTeX[If[e > 0, "+" + e + "y", If[e < 0, "-" + (abs(e)) + "y", ""]]]) + "" + (LaTeX[If[f > 0, "+" + f, If[f < 0, "-" + (-f), ""]]]) + "=0"
text2: "$ ⇒" + (LaTeX[If[d ≟ 0, "", "("]]) + "x^2" + (LaTeX[If[d > 0, "+" + d + "x", If[d < 0, "-" + (abs(d)) + "x", ""]]]) + "" + (LaTeX[If[d ≟ 0, "", ")"]]) + "+" + (LaTeX[If[e ≟ 0, "", "("]]) + "y^2" + (LaTeX[If[e > 0, "+" + e + "y", If[e < 0, "-" + (abs(e)) + "y", ""]]]) + "" + (LaTeX[If[e ≟ 0, "", ")"]]) + "=" + (LaTeX[-f]) + " $"
text3: "$⇒ " + (LaTeX[If[d ≟ 0, "", "("]]) + "x²" + (LaTeX[If[d > 0, "+" + (FractionText[d]) + "x", If[d < 0, "-" + (FractionText[abs(d)]) + "x", ""]]]) + "" + (LaTeX[If[d ≟ 0, "", "+" + (FractionText[(d / 2)^(2)])]]) + "" + (LaTeX[If[d ≟ 0, "", ")"]]) + "+" + (LaTeX[If[e ≟ 0, "", "("]]) + "y²" + (LaTeX[If[e > 0, "+" + (FractionText[e]) + "y", If[e < 0, "-" + (FractionText[abs(e)]) + "y", ""]]]) + "" + (LaTeX[If[e ≟ 0, "", "+" + (FractionText[(e / 2)^(2)])]]) + "" + (LaTeX[If[e ≟ 0, "", ")"]]) + "=" + (LaTeX[FractionText[-f + (d / 2)^(2) + (e / 2)^(2)]]) + " $"
text4: "$ ⇒" + (LaTeX[If[d ≟ 0, "", "("]]) + "x" + (LaTeX[If[d > 0, "+" + (FractionText[abs(d / 2)]), If[d < 0, "-" * FractionText[abs(d / 2)], ""]]]) + "" + (LaTeX[If[d ≟ 0, "", ")"]]) + "²+" + (LaTeX[If[e ≟ 0, "", "("]]) + "y" + (LaTeX[If[e > 0, "+" + (FractionText[abs(e / 2)]), If[e < 0, "-" * FractionText[abs(e / 2)], ""]]]) + "" + (LaTeX[If[e ≟ 0, "", ")"]]) + "²=" + (LaTeX[FractionText[(d^(2) + e^(2) - 4 * f) / 4]]) + " $"