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Tangent of Parabola and Light by Amarzaya

Tangent of Parabola and Light by Amarzaya
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2017-07-18 12:46
FunctionTrigonometryGeometric Construction
This example demonstrates the relationship between the tangent of a parabola and light. Key mathematical concepts include parabolas, tangents, and angles. Using GeoGebra commands such as Parabola, Intersect, If, Point, Vector, and Angle, the construction of the tangent to a parabola and the interaction with light are explored. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Parabola(F_2, x = 0) → d
  2. Intersect(d, j) → H_1,
  3. If(t ≤ 1, H_1) → H
  4. Point(d) → B
  5. Vector(H_1, F_2) → v
  6. Vector(E, H) → u
  7. If(t ≤ 1, ((x(u) * t) + x(E), y(E))) → C
  8. If(t ≥ 1, Tangent[H, d]) → f
  9. Angle(f, Line[F_2, B]) → α
  10. If(t ≥ 1, ((x(v) * (t - 1)) + x(H_1), (y(v) * (t - 1)) + y(H_1))) → D
  11. Point(f) → F
  12. Point(f) → G
  13. If(t ≟ 2, Angle[G, B, F_1]) → γ
  14. Angle(F_2, B, F) → β
  15. Vector(E, C) → g
  16. Vector(H_1, D) → h
  17. If(t ≥ 1, Segment[E, H_1]) → i
  18. If(t ≟ 2, Tangent[H_1, d]) → l

AI Drawing Prompt Reference

Draw a parabola and select a point H on it. Construct the tangent line f at point H. When t is less than or equal to 1, connect point H to focus F2; when t is greater than 1, connect point H to point H1. Adjust the position of the tangent line f and point H based on the value of t, and calculate the angle α between the tangent line f and the line passing through points F2 and B.
The prompt above was compiled from the original drawing commands and is for reference only.