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Ellipse Terminology Demo

Ellipse Terminology Demo
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2017-02-02 09:28
Coordinate GeometryGeometric Construction
This example demonstrates the fundamental geometric properties and terminology of ellipses, covering concepts like definition, foci, major axis, minor axis, eccentricity, and focal radii. It uses commands such as Ray, Point, Rotate, If, Min, Max, Ellipse, Segment, Vector, Circle, and Intersect to construct the ellipse and its elements, making it suitable for high school mathematics instruction and in-depth learning of ellipse knowledge.

GeoGebra Commands & Parameters

  1. Ray(A, C) → j
  2. Point(j) → D
  3. Rotate(D, -90°, A) → D'
  4. Ray(A, D) → h
  5. Ray(D', H) → f
  6. Point(f) → F
  7. If(x(F) ≥ y(D), true, false) → isHorizontal
  8. Min(x(F), y(D)) → b
  9. Max(x(F), y(D)) → a
  10. If(isHorizontal, (c, 0), (0, (-c))) → F_2
  11. Ellipse(F_1, F_2, D) → d
  12. Segment(E, F) → g
  13. Segment(D, G) → i
  14. Point(d) → P
  15. Segment(F_1, P) → l
  16. Segment(F_2, P) → m
  17. Vector(K, I) → u
  18. Vector(K, J) → v
  19. Vector(N, L) → w
  20. Vector(N, M) → e
  21. Ray(A, P) → k
  22. Circle(A, Distance[A, P] + 0.75) → p
  23. Intersect(p, k, 1) → O
  24. Vector(Q_2, T_2) → n
  25. Vector(Q_2, U_2) → q
  26. Vector(Q_1, T_1) → r
  27. Vector(Q_1, U_1) → s