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Unified Definition of Conic Sections

Unified Definition of Conic Sections
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2019-02-21 08:44
Coordinate GeometryGeometric ConstructionLocus
This example demonstrates the unifying definition of conic sections through focus, directrix, and eccentricity. It involves core math concepts like conic sections, eccentricity, focus, directrix, and coordinate geometry. Constructed using GeoGebra commands and objects such as Line, Point, OrthogonalLine, Segment, Intersect, Dilate, Circle, Tangent, Locus, and Angle. Suitable for high school and above mathematics learners to understand the geometric essence and unified definition of conic sections.

GeoGebra Commands & Parameters

  1. Line(A, B) → d
  2. Point(d) → H_1
  3. OrthogonalLine(H_1, d) → b
  4. Segment(F, H_1) → e_1
  5. OrthogonalLine(F, d) → c
  6. Intersect(d, c) → C
  7. Dilate(F, -1 / e, C) → F'
  8. Line(F', H_1) → d_1
  9. Line(C, d_1) → f
  10. Intersect(f, e_1) → D
  11. OrthogonalLine(D, b) → g
  12. Intersect(b, g) → E
  13. Circle(D, E) → h
  14. Tangent(F, h) → i, j
  15. Intersect(b, j) → P_1
  16. Intersect(b, i) → P_2
  17. Locus(P_1, H_1) → luogo1
  18. Locus(P_2, H_1) → luogo2
  19. Point(luogo1) → P
  20. OrthogonalLine(P, d) → a
  21. Intersect(d, a) → H
  22. Segment(P, F) → k
  23. Segment(P, H) → l
  24. Angle(P, H, B) → α