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Hyperbola Reflective Property Demo by Doug Kuhlmann

Hyperbola Reflective Property Demo by Doug Kuhlmann
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2015-06-21 01:30
FunctionCoordinate GeometryGeometric Construction
In collections Conics Doug Kuhlmann
This example demonstrates the reflective property of a hyperbola, where light rays emanating from the foci reflect parallel to the asymptotes. It involves core concepts like hyperbola definition, reflection laws, and coordinate geometry. Construction uses commands such as Hyperbola, Point, Line, Circle, AngularBisector, Segment, Intersect, and Angle. Suitable for high school students and math enthusiasts studying hyperbola properties and geometric constructions.

GeoGebra Commands & Parameters

  1. Hyperbola(F_1, F, C) → c
  2. Point(c) → T
  3. Line(T, F) → d
  4. Circle(T, F) → e
  5. AngularBisector(F_1, T, F) → a
  6. Point(a) → P
  7. Segment(F_1, P) → g
  8. Segment(T, F_1) → b
  9. Segment(F, T) → h
  10. Line(F_1, T) → i
  11. Line(F, T) → j
  12. Intersect(e, b) → F',
  13. Segment(F', P) → m
  14. Segment(F, P) → n
  15. Point(a) → A
  16. Point(a) → B
  17. Point(j) → D
  18. Angle(B, T, D) → α
  19. Angle(F_1, T, A) → β
  20. Point(j) → E
  21. Segment(E, T) → p
  22. Angle(A, T, F) → γ