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Hyperbola Construction and Properties

Hyperbola Construction and Properties
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2016-05-04 10:22
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the construction of a hyperbola and its geometric properties. Key math concepts include the definition of a hyperbola, its standard equation, foci, vertices, and asymptotes. Construction highlights the use of GeoGebra commands like OrthogonalLine, Hyperbola, Point, and Segment, along with objects such as Center, Focus, Vertex, and CoVertex. Suitable for high school mathematics and analytical geometry instruction.

GeoGebra Commands & Parameters

  1. OrthogonalLine(CoVertex_1, xAxis) → g
  2. OrthogonalLine(Vertex_2, g) → i
  3. OrthogonalLine(CoVertex_2, i) → j
  4. OrthogonalLine(Vertex_1, j) → l
  5. Hyperbola(Focus_3, Focus_4, Vertex_4) → c_1
  6. OrthogonalLine(CoVertex_3, yAxis) → a_1
  7. OrthogonalLine(Vertex_4, a_1) → b_1
  8. OrthogonalLine(CoVertex_4, b_1) → d_3
  9. OrthogonalLine(Vertex_3, d_3) → e_1
  10. Point(c_1) → Point_1
  11. Segment(Point_1, Focus_4) → d_1
  12. Segment(Point_1, Focus_3) → d_2
  13. Point(c) → Point
  14. Segment(Focus_1, Point) → d1
  15. Segment(Point, Focus_2) → d2