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Constant Sum to Two Foci

Constant Sum to Two Foci
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2018-04-06 09:29
CircleCoordinate GeometryGeometric Construction
In collections Conic sections
This example demonstrates the geometric figure where the sum of distances to two foci is constant. Key mathematical concepts include the definition and properties of ellipses. Using GeoGebra commands such as Point, Line, Vector, Focus, etc., an ellipse can be constructed. Suitable for high school mathematics education and learning about ellipses.

GeoGebra Commands & Parameters

  1. Point(zAxis) → A
  2. Line(A, B) → f
  3. Vector(A, A + (10 * (B - A))) → u
  4. InfiniteCone(A, u, (π * α / 180)) → a
  5. IntersectPath(d, a) → c
  6. Focus(c) → D, E
  7. OrthogonalLine(D, d) → h
  8. Intersect(h, f) → G
  9. Point(c) → H
  10. Line(A, H) → m
  11. OrthogonalLine(G, m, space) → f_1
  12. OrthogonalLine(E, d) → i
  13. Intersect(i, f) → F
  14. OrthogonalLine(F, m, space) → t
  15. PointIn(a) → C
  16. Line(A, C) → g
  17. Angle(g, f) → β
  18. Sphere(G, D) → b
  19. Sphere(F, E) → e
  20. OrthogonalPlane(F, u) → l
  21. Segment(H, E) → n
  22. Segment(H, D) → q
  23. OrthogonalPlane(G, u) → o
  24. Intersect(t, m) → I
  25. Segment(H, I) → j
  26. Intersect(f_1, m) → J
  27. Segment(J, H) → s
  28. Line(A, A + u) → g_1
  29. Circle(g_1, I) → c_1
  30. Circle(g_1, J) → d_1