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Parabola: Focus Property

Parabola: Focus Property
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2023-03-17 00:50
FunctionCoordinate GeometryGeometric Construction
In collections geometriadinamica.es
This example demonstrates the focus property of a parabola. Key mathematical concepts include the definition of a parabola and the geometric meaning of its focus. Using GeoGebra commands such as OrthogonalLine, Intersect, and Segment, the construction of the parabola and its focus is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, f) → m
  2. Intersect(c, f) → B,
  3. Intersect(c, e) → C,
  4. Intersect(c, d) → D,
  5. Intersect(c, b) → E,
  6. Intersect(c, a) → G,
  7. Intersect(c, g) → H,
  8. Intersect(c, h) → I,
  9. Intersect(c, i) → J,
  10. Intersect(c, j) → K,
  11. Intersect(c, k) → L,
  12. Intersect(c, l) → M,
  13. Intersect(f, m) → N
  14. Intersect(e, m) → O
  15. Intersect(d, m) → P
  16. Intersect(b, m) → Q
  17. Intersect(a, m) → R
  18. Intersect(g, m) → S
  19. Intersect(h, m) → T
  20. Intersect(i, m) → U
  21. Intersect(j, m) → V
  22. Intersect(k, m) → W
  23. Intersect(l, m) → Y
  24. Segment(Z, A_1) → n
  25. OrthogonalLine(Z, n) → q
  26. OrthogonalLine(A_1, n) → r
  27. Point(q) → B_1
  28. OrthogonalLine(B_1, q) → s
  29. Intersect(s, r) → C_1
  30. Point(s) → D_1
  31. Segment(B_1, D_1) → t
  32. Segment(D_1, C_1) → ee
  33. Point(n) → E_1
  34. OrthogonalLine(E_1, n) → b_1
  35. Intersect(t, b_1) → F_1
  36. Intersect(b_1, ee) → G_1
  37. Segment(B_1, F_1) → cc
  38. Segment(NN, N) → c_1
  39. Segment(D_1, G_1) → dd
  40. Segment(NNN, N) → a_1
  41. Segment(B, BF) → d_1
  42. Segment(OO, O) → e_1
  43. Segment(P, P) → f_1
  44. Segment(QQ, Q) → g_1
  45. Segment(PP, P) → h_1
  46. Segment(RR, R) → i_1
  47. Segment(SS, S) → j_1
  48. Segment(TT, T) → k_1
  49. Segment(UU, U) → l_1
  50. Segment(VV, V) → m_1
  51. Segment(WW, W) → n_1
  52. Segment(YY, Y) → p_1
  53. Segment(OOO, O) → q_1
  54. Segment(PPP, P) → r_1
  55. Segment(QQQ, Q) → s_1
  56. Segment(RRR, R) → t_1
  57. Segment(SSS, S) → a_2
  58. Segment(TTT, T) → b_2
  59. Segment(UUU, U) → c_2
  60. Segment(VVV, V) → d_2
  61. Segment(WWW, W) → e_2
  62. Segment(YYY, Y) → f_2
  63. Segment(C, CF) → g_2
  64. Segment(D, DF) → h_2
  65. Segment(E, EF) → i_2
  66. Segment(G, GF) → j_2
  67. Segment(I, IF) → k_2
  68. Segment(J, JF) → l_2
  69. Segment(K, KF) → m_2
  70. Segment(L, LF) → n_2
  71. Segment(M, MF) → p_2

AI Drawing Prompt Reference

Draw a parabola to demonstrate its focus property. First, plot the parabola and identify its focus. Then, draw perpendicular lines from the focus to the parabola, marking the feet of the perpendiculars. Repeat this process to find additional intersection points, and connect these points with line segments to form the parabola's shape.
The prompt above was compiled from the original drawing commands and is for reference only.