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Point on a Hyperbola

Point on a Hyperbola
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2019-08-03 06:19
VectorCoordinate Geometry
This example demonstrates how a point on a hyperbola rotates around two foci. Key mathematical concepts include the definition of a hyperbola, rotation, and vectors. Using GeoGebra commands such as Point, Hyperbola, and Intersect, the construction of the hyperbola and related elements is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(xAxis) → F_1
  2. Point(xAxis) → F_2
  3. Hyperbola(F_1, F_2, C_1) → c
  4. Intersect(a_1, yAxis) → D
  5. Point(a_1) → E
  6. Ray(D, E) → d
  7. Intersect(c, d) → C,
  8. Intersect(b_1, yAxis) → G
  9. Point(b_1) → H
  10. Ray(G, H) → e
  11. Intersect(c, e) → I,
  12. Segment(C, F_2) → h
  13. Circle(F_1, J) → k
  14. Ray(F_1, C) → i
  15. Intersect(k, i) → A,
  16. Segment(C, A) → j
  17. Ray(F_2, I) → b
  18. Circle(F_2, Distance[F_1, J]) → f
  19. Intersect(f, b, 1.0) → B
  20. Segment(F_1, I) → g
  21. Segment(I, B) → l