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Reflective Properties of Conic Sections

Reflective Properties of Conic Sections
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2015-11-12 09:25
Coordinate GeometryGeometric Construction
In collections Conic Sections
This applet demonstrates the special reflective properties of conic sections: ellipse, parabola, and hyperbola. Key mathematical concepts include the geometric properties of conic sections and the principle of reflection. Using GeoGebra commands such as Line, Ray, Point, and Mirror, the applet dynamically illustrates these reflective properties. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(H, G) → l
  2. Ray((0, 0), (1, 0)) → k
  3. Point(k) → B
  4. Mirror(B, yAxis) → B'
  5. Sequence((x(D) + cos(t), y(D) + sin(t)), t, 0, 6.28319, (2 * π / n)) → p
  6. Sequence(Line[D, Element[p, k]], k, 1, n) → rays
  7. Hyperbola(B', B, A) → d
  8. Parabola(B, l) → e
  9. Point(yAxis) → C
  10. Ellipse(B', B, C) → c
  11. If(b, c, If[g, d, If[h, e]]) → f
  12. Sequence(Intersect[f, Element[rays, k], 2], k, 1, n) → ptInt2
  13. Sequence(Intersect[f, Element[rays, k]], k, 1, n) → ptInt
  14. Join({ptInt, ptInt2}) → pp
  15. Sequence(Tangent[Element[pp, k], f], k, 1, n) → tang
  16. Sequence(OrthogonalLine[Element[pp, k], Element[tang, k]], k, 1, n) → norm
  17. Sequence(Mirror[Element[p, k], Element[norm, k]], k, 1, n) → pRef
  18. Distance(B, B') → dist
  19. Sequence(Line[Element[pp, k], Element[pRef, k]], k, 1, n) → refRays
  20. Corner(1) → LL
  21. Polygon(Corner[1], Corner[2], Corner[3], Corner[4]) → poly1, a, i, q, r