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Horizontal Hyperbola Demonstration by hgraber26

Horizontal Hyperbola Demonstration by hgraber26
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2018-02-24 01:25
FunctionCoordinate GeometryGeometric ConstructionSlider AnimationLocus
This example demonstrates the geometric properties and definition of a horizontal hyperbola. It involves core mathematical concepts such as the definition of a hyperbola, asymptotes, foci, vertices, and eccentricity in analytical geometry. Key GeoGebra commands used in construction include Focus, Point, Segment, Asymptote, Intersect, Center, Vertex, OrthogonalLine, Line, Circle, and Polygon to build the hyperbola and its related elements. It is suitable for high school and above students learning analytical geometry, conic sections, and geometric constructions.

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