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Geometric Construction of Ellipse and Hyperbola

Geometric Construction of Ellipse and Hyperbola
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2015-10-22 00:42
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the geometric construction of ellipses and hyperbolas, highlighting their relationships and properties. Key math concepts include definitions of ellipses and hyperbolas, geometric constructions, symmetry, and applications of coordinate geometry. The construction uses GeoGebra commands such as LineBisector, Mirror, Line, Point, Intersect, and AreCollinear, along with Ellipse and Hyperbola objects. Suitable for high school mathematics education to explore the geometric properties and construction methods of conic sections.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → a
  2. Mirror(C, a) → C'
  3. Hyperbola(A, B, C') → p
  4. Ellipse(A, B, C) → c
  5. Line(A, B) → b
  6. Mirror(C, b) → C''
  7. Point(p) → D
  8. Mirror(D, a) → D'
  9. Mirror(D, b) → D''
  10. Line(C', C'') → d
  11. Line(C'', D'') → e
  12. Line(D'', D') → f
  13. Line(D', C) → g
  14. Line(C, D) → h
  15. Line(D, C') → i
  16. Intersect(d, g) → E
  17. Intersect(f, i) → F
  18. Intersect(e, h) → G
  19. AreCollinear(E, F, G) → j
  20. Prove(j) → k