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Ellipse Polar Connection by Josh Berberian

Ellipse Polar Connection by Josh Berberian
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2016-12-07 02:07
Coordinate GeometryGeometric Construction
This example demonstrates the relationship between an ellipse and polar coordinates. Key mathematical concepts include the geometric properties of ellipses and the polar coordinate system. Using GeoGebra commands such as Circle, Point, Line, etc., the polar representation of an ellipse can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Line(A, C) → f
  4. Point(xAxis) → D
  5. Line(C, D) → g
  6. Midpoint(D, C) → E
  7. OrthogonalLine(E, g) → h
  8. Intersect(f, h) → F
  9. Line(D, F) → i
  10. Locus(F, C) → loc1
  11. Midpoint(A, D) → G
  12. OrthogonalLine(G, xAxis) → j
  13. Segment(D, F) → k
  14. Line(F, xAxis) → l
  15. Segment(A, F) → m
  16. OrthogonalLine(E_d, l) → p
  17. Intersect(l, p) → H
  18. Segment(F, H) → q
  19. Distance(D, J) → distanceDJ
  20. Distance(G, J) → distanceGJ
  21. Distance(G, D) → distanceGD
  22. Angle(D, A, F) → α
  23. Vector(A, F) → u
  24. Circle(I, 1) → d
  25. Circle(I, 2) → r
  26. Circle(I, 3) → c_1
  27. Circle(I, 4) → d_1
  28. Circle(I, 5) → e_1
  29. Circle(I, 6) → f_1
  30. Circle(I, 7) → g_1
  31. Circle(I, 8) → h_1
  32. Circle(I, 9) → k_1
  33. Circle(I, 10) → p_1
  34. Circle(I, 11) → q_1
  35. Circle(I, 12) → r_1
  36. Circle(I, 13) → s_1
  37. Circle(I, 14) → t_1
  38. Circle(I, 15) → c_2
  39. Segment(G, K) → b
  40. Segment(G, J) → i_1
  41. Segment(R, S) → j_1
  42. Segment(D, K) → l_1
  43. Midpoint(I, D) → T
  44. Intersect(p, q) → U
  45. Angle(D, I, F) → β
  46. CurveCartesian((cos(t) * E_b^(2) / E_a / (1 - (E_c / E_a * cos(t)))), (sin(t) * E_b^(2) / E_a / (1 - (E_c / E_a * cos(t)))), t, 0, (2 * π)) → w
  47. Distance(D, p) → distanceDp
  48. Intersect(p, xAxis) → V
  49. Segment(S, W) → m_1
  50. Length(u) → a_1
  51. Distance(I, F) → distanceIF
  52. TableText({{A2, B2}, {A3, B3}, {A4, B4}, {A5, B5}, {A6, B6}, {A7, B7}, {A8, B8}, {A9, B9}, {A10, B10}, {A11, B11}, {A12, B12}, {A13, B13}}, "|_") → text1