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Ellipse Exploration

Ellipse Exploration
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2019-04-12 07:33
FunctionCoordinate Geometry
This example demonstrates the geometric properties of an ellipse. Key mathematical concepts include the definition and equation of an ellipse, as well as its relationship to conic sections. Using GeoGebra commands such as OrthogonalLine, Ellipse, and Intersect, one can dynamically explore the properties of the ellipse. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. OrthogonalLine(H, yAxis) → f
  2. Circle(H, mFF' / 2) → p
  3. Intersect(xAxis, yAxis) → B
  4. Circle(B, Corde / 2) → e
  5. Intersect(e, xAxis, 1) → J
  6. Intersect(p, f, 2) → F'
  7. Intersect(p, f, 1) → F
  8. Ellipse(F, F', J) → q
  9. Point(q) → Grat
  10. Segment(F, Grat) → i
  11. Point(Circle[E_1, If[mFF' ≟ 0, Corde / 2, Corde]]) → E_2
  12. Segment(E_1, E_2) → k
  13. Point(Circle[E_1, Length[i]]) → G_1
  14. Segment(E_1, G_1) → l
  15. Segment(G_1, E_2) → m
  16. Segment(F', Grat) → j
  17. Point(Circle[A, 24]) → C
  18. Polygon(A, C, D, E) → P_3, a, c, d, e_1
  19. OrthogonalLine(H, f) → g
  20. If(mFF' ≟ 0, Circle[H, Corde / 2]) → h
  21. Point(h) → Grat_1
  22. Segment(Grat_1, F) → Corde_2
  23. Distance(F, F') → FF'
  24. If(mFF' ≟ 0, Segment[E_1, E_2]) → n
  25. Polygon(E, D, C, A) → q1, e_2, d_1, c_1, a_1
  26. Polygon(I, K, M, O) → q2, i_1, k_1, m_1, o
  27. Polygon(I, Q, R, K) → q3, i_2, q_1, r, k_2
  28. Polygon(Q, G, P, S) → q4, q_2, g_1, p_1, s
  29. Polygon(S, O, M, T) → q5, s_1, o_1, m_2, t
  30. Polygon(R, T, N, L) → q6, r_1, t_1, n_1, l_1