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双曲线与椭圆的图像绘制

双曲线与椭圆的图像绘制
几何画板及绘图内容加载中，请稍等……
2015-06-23 03:30
解析几何
本范例演示如何绘制方程9x^2 – 36x – 4y^2 + 8y = 4的图像。涉及的核心数学概念包括二次曲线的性质和方程的图形表示。通过GeoGebra命令如LaTeX、Polynomial等，可以构造出方程的图像。适合高中数学课程中的解析几何学习。

GeoGebra 命令及参数

  1. LaTeX(steps) → counter
  2. LaTeX("\text{Move the slider to solve the problem.}") → text0
  3. LaTeX("\text{Use the buttons below to return to the original}\cr\text{problem or randomly generate a similar practice}\cr\text{problem.}") → RandomizationText
  4. Corner(1) → A
  5. Corner(3) → B
  6. LaTeX((("\textcolor{#000099}{" * c) * "}")) → Problem
  7. Polynomial((yden / xden * (x - h)) + k) → f
  8. LaTeX((("\textcolor{#000099}{y=" * f) * "}")) → text40
  9. Polynomial((((-yden)) / xden * (x - h)) + k) → g
  10. LaTeX((("\textcolor{#000099}{y=" * g) * "}")) → text40b
  11. Segment(D, E) → d
  12. Segment(F, G) → e
  13. Polygon(C1, C2, C3, C4) → poly1, c1, c2, c3, c4
  14. LaTeX((((((((("\textcolor{#000099}{y-(" * y(C)) * ")=\pm\frac{") * yden) * "}{") * xden) * "}(x-(") * x(C)) * "))}")) → text38
  15. LaTeX((((((((((((((((((((((((("\textcolor{#000099}{" * xfact) * "[x^2-(") * midx) * ")x+") * hsq) * "]") * ypolysign) * "") * yfact) * "[y^2-(") * midy) * ")y+") * ksq) * "]}\cr\text{ }\textcolor{#000099}{ =") * oconst) * "+(") * xfact) * ")(") * hsq) * ")+(") * yfact) * ")(") * ksq) * ")}")) → text12
  16. LaTeX((((((((((((("\textcolor{#000099}{" * xfact) * "[x^2-(") * midx) * ")x+\ldots]") * ypolysign) * "") * yfact) * "[y^2-(") * midy) * ")y+\ldots]=") * oconst) * "}")) → text10
  17. LaTeX((((((((((((("\textcolor{#000099}{" * xfact) * "[x-(") * h) * ")]^2") * ypolysign) * "") * yfact) * "[y-(") * k) * ")]^2 =") * coeffprod) * "}")) → text14
  18. LaTeX((((((((((((((((("\textcolor{#000099}{\frac{" * xfact) * "[x-(") * h) * ")]^2}{") * coeffprod) * "}+\frac{(") * yfact) * ")[y-(") * k) * ")]^2}{") * coeffprod) * "}=\frac{") * coeffprod) * "}{") * coeffprod) * "}}")) → text16
  19. LaTeX((((((((((((("\textcolor{#000099}{" * xsign) * "\frac{[x-(") * h) * ")]^2}{") * xden) * "^2}") * ysign) * "\frac{[y-(") * k) * ")]^2}{") * yden) * "^2}=1}")) → text18
  20. LaTeX((((((((((((("\text{The equation in standard form is }\cr\textcolor{#000099}{" * xsign) * "\frac{[x-(") * h) * ")]^2}{") * xden) * "^2}") * ysign) * "\frac{[y-(") * k) * ")]^2}{") * yden) * "^2}=1}\text{.}")) → text19