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Horizontal Hyperbola Demonstration

Horizontal Hyperbola Demonstration
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2018-02-24 01:42
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the geometric construction of a horizontal hyperbola and its key properties. It involves core mathematical concepts such as the definition of a hyperbola, asymptotes, foci, vertices, and coordinate geometry transformations. Construction highlights include using GeoGebra commands like Focus, Point, Segment, Asymptote, Intersect, Center, Vertex, OrthogonalLine, Line, Circle, and Polygon to build the hyperbola and related elements. Suitable for high school coordinate geometry teaching or exploration by math enthusiasts.

GeoGebra Commands & Parameters

  1. Focus(c_2) → F_2, F_1
  2. Point(c_2) → M_1
  3. Segment(F_1, M_1) → d_1
  4. Segment(F_2, M_1) → d_2
  5. Asymptote(c_2) → i, j
  6. Intersect(j, i) → F
  7. Center(Hyperbola[F_2, F_1, b]) → Center
  8. Vertex(Hyperbola[F_2, F_1, a]) → V_2, V_1, ,
  9. OrthogonalLine(B, xAxis) → e
  10. OrthogonalLine(A, xAxis) → f
  11. Line(V_1, xAxis) → g
  12. Line(V_2, xAxis) → l
  13. Intersect(e, g) → C
  14. Intersect(f, g) → D
  15. Intersect(f, l) → E
  16. Intersect(e, l) → G
  17. Segment(Center, V_1) → a_1
  18. Circle(Center, F_1) → p
  19. Point(p) → H
  20. Segment(Center, H) → m
  21. Segment(Center, H) → n
  22. Point(c_2) → M_2
  23. Segment(F_1, M_2) → d_4
  24. Segment(M_2, F_2) → d_3
  25. Line(V_2, yAxis) → q
  26. Line(V_1, yAxis) → r
  27. Line(I, xAxis) → s
  28. Line(K, xAxis) → t
  29. Intersect(q, s) → L
  30. Intersect(r, s) → M
  31. Intersect(r, t) → N
  32. Intersect(q, t) → O
  33. Polygon(L, M, N, O) → poly2, l_1, b_2, n_1, o
  34. Point(l_1) → J
  35. Intersect(r, s) → P
  36. Segment(V_1, P) → b_1
  37. Segment(Center, P) → c