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General Geometric Definition of Ellipse

General Geometric Definition of Ellipse
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2016-02-14 13:41
Coordinate GeometryGeometric Construction
This example demonstrates the geometric definition of an ellipse by constructing it based on the relationship between its foci and directrix. Key mathematical concepts include the definition of an ellipse, foci, directrix, eccentricity, and geometric construction. The construction utilizes GeoGebra commands such as Circle, Intersect, Segment, OrthogonalLine, Angle, Locus, Point, and Conic. It is suitable for high school students and above to understand the geometric essence of ellipses and the concept of eccentricity.

GeoGebra Commands & Parameters

  1. Circle(B, r) → c
  2. Intersect(c, d, 1) → C
  3. Intersect(c, d, 2) → D
  4. Intersect(c, f, 1) → E
  5. Intersect(c, f, 2) → F
  6. Segment(B, D) → g
  7. OrthogonalLine(D, a) → h
  8. Intersect(a, h) → G
  9. Angle(D, G, A) → α
  10. Segment(D, G) → i
  11. Locus(D, r) → loc1
  12. Locus(C, r) → loc2
  13. Locus(E, r) → loc3
  14. Locus(F, r) → loc4
  15. Point(loc1) → H
  16. Point(loc2) → I
  17. Point(loc2) → J
  18. Conic(I, C, J, D, H) → k