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Segment through a Hyperbola

Segment through a Hyperbola
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2019-05-06 06:03
FunctionCoordinate GeometryGeometric Construction
This example demonstrates constructing a segment through a hyperbola. Key mathematical concepts include hyperbola, segment, intersection, and tangent. It uses commands like Line, Ray, Circle, Rotate, Sequence, Midpoint, Surface, Element, Intersect, and Segment in GeoGebra. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Line(B, A) → g
  2. Ray(F1, F2) → f
  3. Circle(A, Distance[A, C], Vector[(0, 0, 0), (0, 0, 1)]) → c
  4. Rotate(((R * cos(G1)), (R * sin(G1)), Z + H), G2, g) → D
  5. Sequence(Rotate[D, ((i / n * 2) * π), g], i, 1, n) → lista1
  6. Sequence(Rotate[Rotate[(sqrt(x(C)^(2) + y(C)^(2)), 0, z(B)), ((i / n * 2) * π), g], G2, g], i, 1, n) → lista2
  7. Sequence(Segment[Element[lista1, i], Element[lista2, i]], i, 1, Length[lista1]) → lista3
  8. Circle((x(A), y(A), Z), Distance[A, C], Vector[(0, 0, 0), (0, 0, 1)]) → d
  9. Midpoint(Element[lista1, 1], Element[lista2, 1]) → PM
  10. Surface(((aVal * cosh(v)) * cos(u)), ((aVal * cosh(v)) * sin(u)), (cVal * sinh(v)) + Z + H / 2, u, 0, (2 * π), v, (-asinh(H / 2 / cVal)), asinh(H / 2 / cVal)) → b
  11. Surface((aVal * cos(u)), (aVal * sin(u)), v + Z + H / 2, u, 0, (2 * π), v, ((-H)) / 2, H / 2) → e
  12. Surface(((R * (v / (H / 2) - 1)) * cos(u)), ((R * (v / (H / 2) - 1)) * sin(u)), v + Z, u, 0, (2 * π), v, 0, H) → h
  13. Surface(((aVal * cosh(v)) * 0), ((aVal * cosh(v)) * (-1)) + u, (cVal * sinh(v)) + Z + H / 2, v, (-asinh(H / 2 / cVal)), asinh(H / 2 / cVal), u, (-Δ), Δ) → i
  14. Element(lista1, 1) → P1
  15. Element(lista2, 1) → P2
  16. Line(P1, P2) → j
  17. Intersect(j, eq1) → F, G
  18. Segment(A, B) → k