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抛物线、椭圆与双曲线的方程与作图

抛物线、椭圆与双曲线的方程与作图
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2018-08-22 16:59
函数解析几何几何作图
所属专题 Conics
这个范例演示了抛物线、椭圆和双曲线的方程及其几何性质。核心数学概念包括焦点、准线、顶点、轴等。作图要点涉及使用GeoGebra命令如Focus、Directrix、Vertex、Intersect等对象。适合高中生或大学低年级学生用于学习解析几何和函数图像。

GeoGebra 命令及参数

  1. Focus(c19) → F19,
  2. Directrix(c19) → d19,
  3. Vertex(c19) → V19, , ,
  4. Axes(c19) → a19, f20
  5. Intersect(a19, d19) → D19
  6. Point(c19) → M19
  7. Segment(M19, E19) → s191
  8. Segment(M19, F19) → s192
  9. Focus(c20) → F20,
  10. Directrix(c20) → d20,
  11. Axes(c20) → a20, g20
  12. Vertex(c20) → V20, , ,
  13. Intersect(a20, d20) → D20
  14. Point(c20) → M20
  15. Segment(M20, E20) → s201
  16. Segment(M20, F20) → s202
  17. Parabola(F21, d21) → c21
  18. Translate(c21, (3, -2)) → c21'
  19. Vertex(c21) → V21, , ,
  20. Vector(O, V21) → u
  21. Point(xAxis) → F22
  22. Point(xAxis) → F'22
  23. Ellipse(F22, F'22, M22) → c22
  24. Intersect(c22, yAxis) → B22, B'22
  25. Intersect(c22, xAxis) → A22, A'22
  26. Segment(M22, F22) → s221
  27. Segment(M22, F'22) → s222
  28. Point(yAxis) → F'25
  29. Point(yAxis) → F25
  30. Ellipse(F25, F'25, M25_1) → c25_1
  31. Segment(M25_1, F25) → s252_1
  32. Segment(M25_1, F'25) → s251_1
  33. Intersect(c25_1, xAxis) → B25_1, B'25_1
  34. Intersect(c25_1, yAxis) → A25_1, A'25_1
  35. Point(xAxis) → A26
  36. Point(xAxis) → B26
  37. Ellipse(A26, B26, M26) → c26
  38. Intersect(xAxis, yAxis) → D26
  39. Vector(D26, O26) → v
  40. Translate(c26, v) → c'26
  41. Segment(M26, A26) → s261
  42. Segment(M26, B26) → s262
  43. Translate(M26, v) → M'26
  44. Translate(A26, v) → A'26
  45. Translate(M26, v) → C'_1
  46. Translate(A26, v) → A'_1
  47. Segment(C'_1, A'_1) → s'261
  48. Translate(M26, v) → C'_2
  49. Translate(B26, v) → B'26
  50. Segment(C'_2, B'26) → s'262
  51. Point(xAxis) → F27
  52. Point(xAxis) → F'27
  53. Hyperbola(F27, F'27, M27) → c27
  54. Segment(M27, F27) → s271
  55. Segment(M27, F'27) → s272
  56. Intersect(c27, xAxis) → A'27, A27
  57. Point(xAxis) → F29_1
  58. Point(xAxis) → F29
  59. Hyperbola(F29_1, F29, M29) → c29
  60. Intersect(xAxis, yAxis) → D29
  61. Vector(D29, O29) → w
  62. Translate(c29, w) → c'29
  63. Translate(M29, w) → C'
  64. Center(c22) → A
  65. Center(c25_1) → B
  66. Center(c27) → C