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Parabola and Its Properties Demonstration

Parabola and Its Properties Demonstration
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2017-04-27 18:55
FunctionCoordinate GeometryDerivativeGeometric Construction
This example demonstrates the properties of a parabola including its definition, focus, directrix, and tangent lines. It involves core mathematical concepts such as parabola, special points, Pythagorean theorem, subtraction, tangent lines, and hypothesis testing. The construction uses GeoGebra commands like If, OrthogonalLine, Point, Segment, Intersect, and Ray. It is suitable for high school and above students to learn and understand the geometric properties and algebraic applications of parabolas.

GeoGebra Commands & Parameters

  1. If(abs(p) > 0, Parabola[F, r]) → e_1
  2. OrthogonalLine(F, r) → o
  3. Point(e_1) → X1
  4. Segment(F, X1) → f
  5. OrthogonalLine(X1, r) → g
  6. Intersect(r, g) → A
  7. Segment(X1, A) → h
  8. Point(e_1) → X2
  9. Segment(X2, F) → i
  10. OrthogonalLine(X2, r) → j
  11. Intersect(r, j) → B
  12. Segment(X2, B) → k
  13. Segment(F, V) → n
  14. Intersect(r, o) → C
  15. Segment(V, C) → m
  16. OrthogonalLine(F, o) → s
  17. Intersect(kx, s, 1) → E
  18. Segment(E, F) → t
  19. Ray(LP, pv) → hd
  20. Ray(L_5, pv) → h_5
  21. Ray(L_4, pv) → h_4
  22. Ray(L_3, pv) → h_3
  23. Ray(L_2, pv) → h_2
  24. Ray(L_1, pv) → h_1
  25. Ray(P_5, pv) → d_5
  26. Ray(P_4, pv) → d_4
  27. Ray(P_3, pv) → d_3
  28. Ray(P_2, pv) → d_2
  29. Ray(P_1, pv) → d_1
  30. Segment(L_1, F) → l_1
  31. Segment(L_2, F) → l_2
  32. Segment(L_3, F) → l_3
  33. Segment(L_4, F) → l_4
  34. Segment(L_5, F) → l_5
  35. Segment(LP, F) → lp
  36. Segment(P_1, F) → p_1
  37. Segment(P_2, F) → p_2
  38. Segment(P_3, F) → p_3
  39. Segment(P_4, F) → p_4
  40. Segment(P_5, F) → p_5
  41. Ray(P_0, pv) → d_0
  42. Ray(L_0, pv) → h_0
  43. Segment(L_0, F) → l_0
  44. Segment(P_0, F) → p_0