Reflective Property of a Parabola

Reflective Property of a Parabola
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2016-11-01 08:16
This example demonstrates the reflective property of a parabola, where the angle between the line from any point on the parabola to its focus and the perpendicular from that point to the directrix are equal. Key math concepts include parabola definition, focus, directrix, perpendicular lines, and angle equality. It is constructed using GeoGebra commands like Point, OrthogonalLine, Parabola, Tangent, Intersect, Segment, Line, Ray, Angle, and Rotate. Suitable for high school students learning analytical geometry to visually understand and apply the reflective property of parabolas.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. OrthogonalLine(A, yAxis) → Directrix
  3. Point(yAxis) → Focus
  4. Parabola(Focus, Directrix) → c
  5. Point(c) → C
  6. Tangent(C, c) → g,
  7. OrthogonalLine(C, g) → h
  8. Intersect(h, yAxis) → D
  9. Segment(C, D) → i
  10. Line(C, yAxis) → j
  11. Point(j) → E
  12. Ray(C, E) → k
  13. Angle(D, C, E) → α
  14. Rotate(D, (-α), C) → D'_1
  15. Angle(D'_1, C, D) → α'
  16. Ray(C, Focus) → l
  17. Rotate(D, α, C) → D'
  18. Angle(D, C, D') → β