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Conic Sections: Ellipse, Parabola, Hyperbola

Conic Sections: Ellipse, Parabola, Hyperbola
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2018-07-08 10:32
VectorCoordinate GeometryGeometric Construction
This example demonstrates the formation and properties of conic sections including ellipse, parabola, and hyperbola. Key math concepts involved are the definition of conic sections, standard equations, geometric properties, and applications of vectors and angles. Construction highlights include using GeoGebra commands like Circle, Point, and LineBisector as per the summary. Suitable for high school mathematics students and educational purposes needing visual understanding of conic sections' geometric essence.

GeoGebra Commands & Parameters

  1. Circle(center, m) → c
  2. Point(c) → n
  3. Circle(center_1, m_1) → c_1
  4. Point(c) → A
  5. Point(c) → B
  6. Point(c) → D
  7. Point(c) → E
  8. Point(c) → F
  9. Point(c) → G
  10. Point(c) → H
  11. Point(c) → I
  12. Point(c) → J
  13. Point(c) → K
  14. Point(c) → L
  15. Point(c) → M
  16. Point(c) → N
  17. Point(c) → O
  18. LineBisector(M, pointie) → g_1
  19. LineBisector(N, pointie) → h_1
  20. LineBisector(O, pointie) → i_1
  21. LineBisector(L, pointie) → j_1
  22. LineBisector(K, pointie) → k_1
  23. LineBisector(J, pointie) → l_1
  24. LineBisector(I, pointie) → n_1
  25. LineBisector(H, pointie) → p_1
  26. LineBisector(G, pointie) → q_1
  27. LineBisector(F, pointie) → r_1
  28. LineBisector(E, pointie) → s_1
  29. LineBisector(D, pointie) → t_1
  30. LineBisector(B, pointie) → b_1
  31. LineBisector(A, pointie) → d_1
  32. LineBisector(pointie, m) → e_1
  33. LineBisector(pointie, n) → f_2
  34. Point(c) → Q
  35. Point(c) → R
  36. Point(c) → T
  37. Point(c) → U
  38. Point(c) → W
  39. LineBisector(Q, pointie) → g_2
  40. LineBisector(R, pointie) → h_2
  41. LineBisector(T, pointie) → i_2
  42. LineBisector(U, pointie) → j_2
  43. LineBisector(W, pointie) → k_2
  44. Point(c) → Z
  45. LineBisector(pointie, Z) → l_2
  46. Point(c) → P
  47. LineBisector(P, pointie) → f
  48. Point(c) → C
  49. LineBisector(C, pointie) → g
  50. Point(c) → S
  51. LineBisector(S, pointie) → h