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椭圆极线关联

椭圆极线关联
几何画板及绘图内容加载中，请稍等……
2016-12-07 04:08
解析几何几何作图
这个范例演示了椭圆与极线之间的关联。核心数学概念包括椭圆的几何性质和极线的定义。通过使用GeoGebra命令如Circle, Point, Line, Intersect等，可以构造出椭圆及其极线。适合高中数学教学，特别是解析几何和圆锥曲线的学习。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Line(A, C) → f
  4. Point(xAxis) → D
  5. Line(C, D) → g
  6. Midpoint(D, C) → E
  7. OrthogonalLine(E, g) → h
  8. Intersect(f, h) → F
  9. Line(D, F) → i
  10. Locus(F, C) → loc1
  11. Midpoint(A, D) → G
  12. OrthogonalLine(G, xAxis) → j
  13. Segment(D, F) → k
  14. Line(F, xAxis) → l
  15. Segment(A, F) → m
  16. OrthogonalLine(E_d, l) → p
  17. Intersect(l, p) → H
  18. Segment(F, H) → q
  19. Distance(D, J) → distanceDJ
  20. Distance(G, J) → distanceGJ
  21. Distance(G, D) → distanceGD
  22. Angle(D, A, F) → α
  23. Vector(A, F) → u
  24. Circle(I, 1) → d
  25. Circle(I, 2) → r
  26. Circle(I, 3) → c_1
  27. Circle(I, 4) → d_1
  28. Circle(I, 5) → e_1
  29. Circle(I, 6) → f_1
  30. Circle(I, 7) → g_1
  31. Circle(I, 8) → h_1
  32. Circle(I, 9) → k_1
  33. Circle(I, 10) → p_1
  34. Circle(I, 11) → q_1
  35. Circle(I, 12) → r_1
  36. Circle(I, 13) → s_1
  37. Circle(I, 14) → t_1
  38. Circle(I, 15) → c_2
  39. Segment(G, K) → b
  40. Segment(G, J) → i_1
  41. Segment(R, S) → j_1
  42. Segment(D, K) → l_1
  43. Midpoint(I, D) → T
  44. Intersect(p, q) → U
  45. Angle(D, I, F) → β
  46. CurveCartesian((cos(t) * E_b^(2) / E_a / (1 - (E_c / E_a * cos(t)))), (sin(t) * E_b^(2) / E_a / (1 - (E_c / E_a * cos(t)))), t, 0, (2 * π)) → w
  47. Distance(D, p) → distanceDp
  48. Intersect(p, xAxis) → V
  49. Segment(S, W) → m_1
  50. Length(u) → a_1
  51. Distance(I, F) → distanceIF
  52. TableText({{A2, B2}, {A3, B3}, {A4, B4}, {A5, B5}, {A6, B6}, {A7, B7}, {A8, B8}, {A9, B9}, {A10, B10}, {A11, B11}, {A12, B12}, {A13, B13}}, "|_") → text1