Ellipse & Hyperbola Construction by Circle

Ellipse & Hyperbola Construction by Circle
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2015-07-08 04:35
This example demonstrates how to construct ellipses and hyperbolas using circle geometry. It involves core mathematical concepts such as circles, ellipses, hyperbolas, and their definitions in analytic geometry. Key construction steps include using GeoGebra commands like Circle, Point, Ray, LineBisector, Intersect, Ellipse, Segment, Angle, PolyLine, Distance, and Hyperbola. Suitable for high school students and teachers to understand the geometric construction of conic sections and their practical applications.

GeoGebra Commands & Parameters

  1. Circle(A, df) → p
  2. Point(p) → G
  3. Ray(A, G) → l
  4. Circle(A, rd) → c
  5. Point(c) → C
  6. Ray(A, C) → a
  7. LineBisector(B, C) → b
  8. Intersect(b, a) → D
  9. Ellipse(A, B, D) → d
  10. Segment(C, B) → e
  11. Angle(b, e) → α
  12. Intersect(b, e) → F
  13. Segment(C, F) → f
  14. Segment(F, B) → g
  15. PolyLine(A, D, B) → h
  16. Distance(A, B) → base
  17. Segment(D, C) → i
  18. LineBisector(G, B) → j
  19. Intersect(l, j) → H
  20. Hyperbola(B, A, H) → k
  21. Circle(H, B) → q