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Vertical Hyperbola

Vertical Hyperbola
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2018-02-24 01:24
FunctionCoordinate GeometryTransformation
This example demonstrates the geometric construction and properties of a vertical hyperbola. Key math concepts include the definition of a hyperbola, foci, vertices, asymptotes, and eccentricity. Construction involves GeoGebra commands like Focus, Point, Segment, Asymptote, Intersect, Center, Vertex, OrthogonalLine, Line, Polygon, Circle. 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. Point(c_2) → M_2
  6. Segment(F_2, M_2) → d_4
  7. Segment(M_2, F_1) → d_3
  8. Asymptote(c_2) → i, j
  9. Intersect(j, i) → F
  10. Center(Hyperbola[F_2, F_1, b]) → Center
  11. Vertex(Hyperbola[F_2, F_1, a]) → V_2, V_1, ,
  12. OrthogonalLine(B, xAxis) → e
  13. OrthogonalLine(A, xAxis) → f
  14. Line(V_1, xAxis) → g
  15. Line(V_2, xAxis) → l
  16. Intersect(e, g) → C
  17. Intersect(f, g) → D
  18. Intersect(f, l) → E
  19. Intersect(e, l) → G
  20. Polygon(C, D, E, G) → poly1, c_1, d_6, e_1, g_1
  21. Segment(Center, V_1) → a_1
  22. Segment(V_1, C) → b_1
  23. Circle(Center, F_1) → p
  24. Point(p) → H
  25. Segment(Center, H) → m
  26. Intersect(c_1, b_1) → I
  27. Intersect(g_1, c_1) → J
  28. Segment(Center, J) → c
  29. Segment(Center, H) → n