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Collinear Image of a Circle - Ellipse Case

Collinear Image of a Circle - Ellipse Case
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2015-12-01 21:27
Circle
This example demonstrates the collinear image of a circle in the case of an ellipse. Key mathematical concepts include circles, ellipses, collinear images, and transformations. Using GeoGebra commands such as Line, Circle, Intersect, etc., the construction of the collinear image of a circle is illustrated. Suitable for high school mathematics education, particularly in coordinate geometry and transformations.

GeoGebra Commands & Parameters

  1. Line(A_1, B_1) → osa
  2. Line(C_1, osa) → úběžnice
  3. Circle(O, E) → c
  4. OrthogonalLine(O, osa) → p
  5. Intersect(c, p) → Q, R
  6. OrthogonalLine(R, p) → t_1
  7. OrthogonalLine(Q, p) → t_2
  8. Intersect(úběžnice, p) → U
  9. Line(S, U) → U_∞
  10. Intersect(osa, p) → D_1
  11. Line(D_1, U_∞) → p'
  12. Line(S, R) → b
  13. Line(S, Q) → d
  14. Intersect(p', b) → R'
  15. Intersect(d, p') → Q'
  16. Segment(Q', R') → e
  17. Midpoint(Q', R') → P'
  18. Line(S, P') → f
  19. Intersect(p, f) → P
  20. Line(P, osa) → g
  21. Intersect(c, g) → M, N
  22. Segment(Q, R) → h
  23. Segment(M, N) → i
  24. Line(Q', osa) → t'_2
  25. Line(R', osa) → t'_1
  26. Line(P', osa) → j
  27. Line(S, M) → k
  28. Line(S, N) → l
  29. Intersect(j, k) → M'
  30. Intersect(l, j) → N'
  31. Segment(M', N') → m
  32. Point(c) → A
  33. Line(S, A) → a
  34. Line(R, A) → n
  35. Intersect(n, osa) → B
  36. Line(B, R') → q
  37. Intersect(a, q) → A'
  38. Conic(M', R', N', Q', A') → r
  39. Intersect(c, r) → C, D, F, G
  40. Line(S, A') → s