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Dynamic Parabola Focal Chord Action

Dynamic Parabola Focal Chord Action
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2017-05-04 06:25
VectorCoordinate GeometryGeometric Construction
In collections Conic Sections
This example dynamically demonstrates the geometric properties of a special focal chord inside a parabola. It involves core math concepts like parabola, ratios, 3D vectors, curve sketching, binomial distribution, and indefinite integral. Construction highlights include commands like Line, Parabola, Point, OrthogonalLine, Intersect, Dilate, Segment, Angle, Rotate, Circle, and Ray. Suitable for high school mathematics students and teachers exploring dynamic relationships and geometric transformations of parabolas and focal chords.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Parabola(C, a) → c
  3. Point(c) → D
  4. OrthogonalLine(D, a) → b
  5. Intersect(a, b) → E
  6. Dilate(C, If[0 < d ≤ 1, 1 - d, 0], D) → C'
  7. Segment(C, C') → e
  8. Dilate(D, If[1 < d ≤ 2, 2 - d, 0], E) → D'
  9. Segment(D, D') → f
  10. Angle(A, E, D) → α
  11. Angle(E, D, C) → β
  12. Rotate(C, If[2 < d ≤ 3, ((-(d - 2)) * β), (-β)], D) → C'_1
  13. Rotate(C', If[2 < d ≤ 3, ((-(d - 2)) * β), (-β)], D) → C''
  14. Segment(C'_1, C'') → e'
  15. OrthogonalLine(C, a) → g
  16. Intersect(c, g) → V, S
  17. OrthogonalLine(C, g) → h
  18. Intersect(c, h) → G, H
  19. Circle(C, 2) → k
  20. Intersect(k, c, 1) → I
  21. Intersect(k, c, 1) → J
  22. Intersect(k, g) → K, L
  23. Segment(V, C) → i
  24. Circle(G, i) → p
  25. Intersect(p, h) → F, M
  26. Circle(H, i) → q
  27. Intersect(q, h) → N, O
  28. Ray(C, L) → j
  29. Angle(M, C, L) → γ
  30. Dilate(V, If[3 < d ≤ 4, 4 - d, 0], C) → V'
  31. Segment(V, V') → l
  32. Dilate(G, If[5 < d ≤ 6, 6 - d, 0], M) → G'
  33. Segment(G, G') → m
  34. Dilate(M, If[6 < d ≤ 7, 7 - d, 0], C) → M'
  35. Segment(M, M') → n
  36. Dilate(C, If[7 < d ≤ 8, 8 - d, 0], N) → C'_2
  37. Segment(C, C'_2) → r
  38. Dilate(N, If[8 < d ≤ 9, 9 - d, 0], H) → N'
  39. Segment(N, N') → s
  40. Rotate(V, If[9 < d ≤ 10, ((d - 9) * π / 2), π / 2], C) → V'_1
  41. Rotate(V', If[9 < d ≤ 10, ((d - 9) * π / 2), π / 2], C) → V''
  42. Segment(V'_1, V'') → l'
  43. Rotate(V, If[9 < d ≤ 10, ((-(d - 9)) * π / 2), ((-π)) / 2], C) → V'_2
  44. Rotate(V', If[9 < d ≤ 10, ((-(d - 9)) * π / 2), ((-π)) / 2], C) → V''_1
  45. Segment(V'_2, V''_1) → l'_1
  46. Rotate(V'_1, If[10 < d ≤ 11, ((d - 10) * π), π], M) → P
  47. Rotate(V'', If[10 < d ≤ 11, ((d - 10) * π), π], M) → V'''
  48. Segment(P, V''') → l''
  49. Rotate(V'_2, If[10 < d ≤ 11, ((d - 10) * π), π], N) → Q
  50. Rotate(V''_1, If[10 < d ≤ 11, ((d - 10) * π), π], N) → R
  51. Segment(Q, R) → t