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Leibniz Parabola - Move Secant to Tangent Position

Leibniz Parabola - Move Secant to Tangent Position
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2015-04-19 15:07
FunctionCoordinate GeometryDerivativeSlider AnimationLocus
This example demonstrates the transition from a secant to a tangent on a parabola by moving sliders Y_1 and Y_2. Key mathematical concepts include the properties of parabolas and derivatives. GeoGebra commands used include Line, Point, Parabola, Intersect, Segment, OrthogonalLine, and Ray. Suitable for high school mathematics, particularly calculus and coordinate geometry courses.

GeoGebra Commands & Parameters

  1. Line(A_1, B) → a
  2. Point(yAxis) → C
  3. Parabola(C, a) → c
  4. Point(c) → Y_1
  5. Point(c) → Y_2
  6. Intersect(c, xAxis, 1) → A
  7. Line(A, a) → b
  8. Line(Y_1, Y_2) → d
  9. Line(Y_1, yAxis) → e
  10. Line(Y_2, yAxis) → f
  11. Intersect(b, e) → X_1
  12. Segment(Y_1, X_1) → g
  13. Intersect(b, f) → X_2
  14. Segment(Y_2, X_2) → h_2
  15. OrthogonalLine(Y_1, g) → i
  16. Intersect(i, h_2) → D
  17. Segment(Y_1, D) → j
  18. Ray(Y_1, D) → k
  19. Line(Y_2, b) → l
  20. Point(l) → J
  21. Ray(Y_2, J) → m
  22. Line(K, h_2) → n
  23. Intersect(n, m) → L
  24. Intersect(n, k) → M
  25. Segment(L, M) → ΔY
  26. Point(b) → N
  27. Segment(M, N) → Y
  28. Line(Y_1, yAxis) → r
  29. Line(D, yAxis) → s
  30. Line(O, b) → t
  31. Intersect(r, t) → P
  32. Intersect(s, t) → Q
  33. Segment(P, Q) → ΔX
  34. Intersect(t, yAxis) → R
  35. Segment(R, P) → X
  36. OrthogonalLine(P, X) → p
  37. Point(p) → S
  38. Point(p) → T_1
  39. Ray(Y_1, D) → q
  40. Ray(Y_2, L) → a_1
  41. Ray(Y_1, X_1) → b_1
  42. Ray(Y_2, D) → c_1
  43. Point(c) → E
  44. Point(c) → F
  45. Segment(E, F) → d_1
  46. OrthogonalLine(A, b) → e_1
  47. Point(c) → G
  48. Segment(C, G) → f_1
  49. OrthogonalLine(G, a) → g_1
  50. Intersect(a, g_1) → H
  51. Segment(G, H) → h_1
  52. Intersect(b, d) → T
  53. Segment(T, X_1) → h