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Equations of Conics

Equations of Conics
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2018-08-22 16:59
FunctionCoordinate GeometryGeometric Construction
In collections Conics
This example demonstrates the equations of parabolas, ellipses, and hyperbolas, highlighting their geometric properties. Key mathematical concepts include focus, directrix, vertex, and axes. Construction involves GeoGebra commands such as Focus, Directrix, Vertex, and Intersect with relevant objects. Suitable for high school students or college freshmen learning analytic geometry and graphing functions.

GeoGebra Commands & Parameters

  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