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Reflection Property of a Parabola by tcoe

Reflection Property of a Parabola by tcoe
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2011-09-23 04:24
FunctionGeometric Construction
In collections Parabola - focus and directrix
This example demonstrates an animation of the reflection property of a parabola. Key mathematical concepts include parabola, reflection, function graphing, and geometric construction. Construction involves using GeoGebra commands like Intersect, OrthogonalLine, Tangent, Mirror, and objects such as focus, parabola equation. Suitable for high school students or math enthusiasts to understand parabola properties and geometric transformations.

GeoGebra Commands & Parameters

  1. Intersect(f, b, 1) → C
  2. Intersect(f, b, 2) → D
  3. OrthogonalLine(C5, b) → c
  4. OrthogonalLine(C6, b) → d
  5. OrthogonalLine(C7, b) → e
  6. OrthogonalLine(C8, b) → g
  7. OrthogonalLine(C9, b) → h
  8. OrthogonalLine(C10, b) → i
  9. OrthogonalLine(C11, b) → j
  10. OrthogonalLine(D, b) → k
  11. Intersect(f, c, 1) → E
  12. Intersect(f, d, 1) → F
  13. Intersect(f, e, 1) → G
  14. Intersect(f, h, 1) → H
  15. Intersect(f, i, 1) → I
  16. Intersect(f, j, 1) → J
  17. Tangent(E, f) → m
  18. Tangent(F, f) → n
  19. Tangent(G, f) → p
  20. Tangent(A, f) → q
  21. Tangent(H, f) → r
  22. Tangent(I, f) → s
  23. Tangent(J, f) → t
  24. Tangent(D, f) → a_1
  25. Tangent(C, f) → b_1
  26. Mirror(c, m) → c'
  27. Mirror(d, n) → d'
  28. Mirror(e, p) → e'
  29. Mirror(C, b_1) → C'
  30. OrthogonalLine(C, b) → c_1
  31. Mirror(c_1, b_1) → d_1
  32. Mirror(k, a_1) → k'
  33. Mirror(j, t) → j'
  34. Mirror(i, s) → i'
  35. Mirror(h, r) → h'
  36. Mirror(B13, b_1) → B13'
  37. Mirror(B15, m) → B15'
  38. Mirror(B16, n) → B16'
  39. Mirror(B17, p) → B17'
  40. Mirror(B19, r) → B19'
  41. Mirror(B20, s) → B20'
  42. Mirror(B21, t) → B21'
  43. Mirror(B18, q) → B18'
  44. Mirror(D, a_1) → D'
  45. Mirror(B23, a_1) → B23'