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Ellipse Tangent and Light

Ellipse Tangent and Light
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2017-07-18 12:38
VectorTrigonometryCoordinate GeometryGeometric Construction
In collections Conic sections
This example demonstrates the geometric relationship between the tangent of an ellipse and light reflection. It involves core math concepts like the definition of an ellipse, tangent equations, vector operations, and reflection laws. Construction uses GeoGebra commands: Ellipse, Point, Vector, If, Angle. Suitable for high school and above students studying analytical geometry, vectors, and optical principles.

GeoGebra Commands & Parameters

  1. Ellipse(F_1, F_2, A) → d
  2. Point(d) → B
  3. Vector(F_2, B) → u
  4. Vector(B, F_1) → v
  5. If(t ≤ 1, ((x(u) * t) + x(F_2), (y(u) * t) + y(F_2))) → C
  6. If(t ≥ 1, Tangent[B, d]) → f
  7. Angle(f, Line[F_2, B]) → α
  8. If(t ≥ 1, ((x(v) * (t - 1)) + x(B), (y(v) * (t - 1)) + y(B))) → D
  9. If(t ≥ 1, Segment[F_2, B]) → i
  10. Vector(B, D) → h
  11. Vector(F_2, C) → g
  12. Point(f) → F
  13. Point(f) → G
  14. If(t ≟ 2, Angle[G, B, F_1]) → γ
  15. Angle(F_2, B, F) → β