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Ellipse Terminology: Foci, Axes, and Geometric Properties

Ellipse Terminology: Foci, Axes, and Geometric Properties
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2017-02-02 09:33
VectorCoordinate GeometryTransformationGeometric ConstructionLocus
This GeoGebra example demonstrates the fundamental terminology and geometric definition of an ellipse. Key mathematical concepts include foci, major axis, minor axis, focal distance, and eccentricity. Construction utilizes commands such as Ellipse, Point, Segment, Intersect, and Vector to visualize the relationship between the curve and its defining elements. Suitable for high school geometry classes or self-study on conic sections, aiding in understanding the geometric meaning behind the standard equation.

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