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垂直抛物线：焦点、准线与焦点弦

垂直抛物线：焦点、准线与焦点弦
几何画板及绘图内容加载中，请稍等……
2015-05-31 05:23
函数解析几何几何作图滑块动画
①本范例演示垂直抛物线的几何性质，包括焦点、准线、焦点弦的动态关系；②涉及核心数学概念：抛物线定义、焦点-准线距离、焦点弦长度、解析几何；③作图要点：使用 GeoGebra 命令 Point（点）、OrthogonalLine（垂线）、Intersect（交点）、Segment（线段）、Angle（角度）、Distance（距离）、Line（直线）、Midpoint（中点）等构建抛物线及其相关元素；④适合高中解析几何教学或数学爱好者探索抛物线性质。

GeoGebra 命令及参数

  1. Point(Directrix) → RandomPointonDirectrix
  2. OrthogonalLine(RandomPointonDirectrix, Directrix) → b
  3. Intersect(c, b) → B, D
  4. Segment(Focus, B) → d
  5. Point(Directrix) → C
  6. Angle(B, RandomPointonDirectrix, C) → α
  7. Segment(RandomPointonDirectrix, B) → e
  8. Distance(Focus, B) → distanceFocusB
  9. Distance(RandomPointonDirectrix, B) → distanceAB
  10. Segment(Focus, D) → f
  11. Segment(RandomPointonDirectrix, D) → g
  12. Angle(C, RandomPointonDirectrix, D) → β
  13. Distance(Focus, D) → distanceFocusD
  14. Distance(D, RandomPointonDirectrix) → distanceDRandomPointonDirectrix
  15. Segment(Focus, Vertex) → i
  16. OrthogonalLine(Vertex, Directrix) → j
  17. Intersect(j, Directrix) → A
  18. Segment(A, Vertex) → l
  19. Distance(Focus, Vertex) → distanceFocusVertex
  20. Distance(Vertex, A) → distanceVertexA
  21. Line(Focus, Directrix) → m
  22. Intersect(c, m) → E, F
  23. Segment(E, F) → n
  24. Segment(E, F) → q
  25. Distance(E, F) → distanceEF
  26. Midpoint(E, F) →
  27. Distance(Vertex, Focus) → distanceVertexFocus
  28. Midpoint(Vertex, Focus) →
  29. Distance(Vertex, A) → a
  30. Midpoint(Vertex, A) →