椭圆方程绘制练习
几何画板及绘图内容加载中,请稍等……
①本范例演示如何通过动态交互绘制椭圆方程;②涉及核心数学概念包括椭圆的定义、标准方程、参数方程以及坐标几何;③构造过程中运用了RandomElement, Random, If, Element, Ellipse等GeoGebra命令和对象,如通过滑块动态调整椭圆参数;④适合高中数学教学,用于帮助学生理解椭圆方程的几何意义和参数变化对图形的影响。
GeoGebra 命令及参数
RandomElement(L_4) → sRandom(-9, 9) → k1Random(-9, 9) → hIf(k1 ≟ 0 ∧ h ≟ 0, k1 + 1, k1) → kRandom(1, 6) → nElement(L_3, n) → aElement(L_2, n) → bElement(L_1, n) → cIf(k > 0, "(" + "y-" + k + ")²", If[k < 0, "(" + "y+" + (((-k) * ")²")), "y²"]) → text2If(h > 0, "(" + "x-" + h + ")²", If[h < 0, "(" + "x+" + (((-h) * ")²")), "x²"]) → text1If(h > 0, "(" + "x+" + h + ")²", If[h < 0, "(" + "x-" + (((-h) * ")²")), "x²"]) → text3If(k > 0, "(" + "y+" + k + ")²", If[k < 0, "(" + "y-" + (((-k) * ")²")), "y²"]) → text4If(h > 0, "-" + (abs(((2 * h) * b2))) + "x", If[h < 0, "+" + (abs(((2 * h) * b2))) + "x", ""]) → text10If(d < 0, "-" + (abs((-d))), If[d > 0, "+" + d, ""]) → text12If(k > 0, "-" + (abs(((2 * k) * a2))) + "y", If[k < 0, "+" + (abs(((2 * k) * a2))) + "y", ""]) → text11If(h > 0, "-" + (abs(((2 * h) * a2))) + "x", If[h < 0, "+" + (abs(((2 * h) * a2))) + "x", ""]) → text15If(k > 0, "-" + (abs(((2 * k) * b2))) + "y", If[k < 0, "+" + (abs(((2 * k) * b2))) + "y", ""]) → text16If(e < 0, "-" + (abs((-e))), If[e > 0, "+" + e, ""]) → text17If(e1 < 0, "-" + (abs((-e1))), If[e1 > 0, "+" + e1, ""]) → text171If(d1 < 0, "-" + (abs((-d1))), If[d1 > 0, "+" + d1, ""]) → text121If(n_1 ≟ 1, Random[1, 2], If[n_1 ≟ 2, Random[3, 4], Random[1, 4]]) → fIf(f ≟ 1, t01, If[f ≟ 2, t21, If[f ≟ 3, t11, t31]]) → t001If(f ≟ 1, t02, If[f ≟ 2, t22, If[f ≟ 3, t12, t32]]) → t002If(f ≟ 1, t03, If[f ≟ 2, t23, If[f ≟ 3, t13, t33]]) → t003If(f ≟ 1, t04, If[f ≟ 2, t24, If[f ≟ 3, t14, t34]]) → t004Random(1, 4) → iEllipse(FX1, FX2, a) → pEllipse(FY1, FY2, a) → qIf(g ≟ 1, "A", If[g ≟ 2, "B", If[g ≟ 3, "C", "D"]]) → text44If(i ≟ 1, "A", If[i ≟ 2, "B", If[i ≟ 3, "C", "D"]]) → text45If(n_1 ≟ 1, "สมการมาตรฐาน", If[n_1 ≟ 2, "สมการทั่วไป", "แบบระคน"]) → text48
AI 绘图提示语参考
绘制一个动态椭圆,通过滑块调整其参数,展示标准方程和参数方程。椭圆中心在坐标系中,长轴和短轴长度可变。动态显示椭圆的参数方程和标准方程,并标注焦点和顶点位置。
以上提示语为根据原始绘图命令整理而来,仅供参考。