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Ellipse Locus Construction

Ellipse Locus Construction
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2018-02-21 09:58
Coordinate GeometryGeometric ConstructionLocus
This example demonstrates the geometric construction of an ellipse as a locus using dynamic geometry principles. Key math concepts include similar triangles, circles, parametric equations, and coordinate geometry. Construction involves GeoGebra commands such as Intersect, Circle, Point, Segment, OrthogonalLine, Locus, Ray, Angle, and Midpoint, with objects like points A, B, C, and parameters a, b. Suitable for high school mathematics education or for enthusiasts studying ellipse construction techniques.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, a) → c
  3. Circle(A, b) → d
  4. Point(d) → C'
  5. Intersect(d, yAxis, 2) → D
  6. Intersect(c, yAxis, 2) → E
  7. Intersect(d, xAxis, 2) → G
  8. Intersect(c, xAxis, 2) → H
  9. Intersect(c, yAxis, 1) → I
  10. Intersect(d, yAxis, 1) → J
  11. Segment(A, C') → g
  12. Intersect(c, g, 1) → K
  13. OrthogonalLine(K, xAxis) → h
  14. OrthogonalLine(C', h) → i
  15. Intersect(i, h) → L
  16. Locus(L, C') → loc1
  17. Intersect(h, xAxis) → F
  18. Intersect(i, yAxis) → M
  19. Segment(A, M) → f
  20. Segment(A, F) → j
  21. Ray((0, 0), (1, 0)) → PlusXAxis
  22. Angle(PlusXAxis, g) → α
  23. Midpoint(A, M) → N
  24. Midpoint(A, F) → O