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Finding Ellipse Equations by Graphing

Finding Ellipse Equations by Graphing
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2019-01-07 13:18
FunctionCoordinate GeometryGeometric ConstructionGraphing
This example demonstrates how to find ellipse equations through graphing. It involves core math concepts like ellipses, equations, vectors, angles, polynomial functions, linear functions, and rectangles. Key GeoGebra commands used include RandomElement, If, Random, Hyperbola, Asymptote, Line, Intersect, and Segment. Suitable for high school mathematics teaching, helping students understand the drawing and solving of ellipse equations.

GeoGebra Commands & Parameters

  1. RandomElement(L_1) → h1
  2. RandomElement(L_1) → k
  3. If(h1 ≟ k, 9, h1) → h
  4. Random(2, 12) → a
  5. Random(1, 5) → f1
  6. Random(1, 2) → b
  7. Hyperbola(E, D, B) → c
  8. Hyperbola(I, H, F) → d
  9. If(b ≟ 1, text3, text5) → t1
  10. If(b ≟ 1, text4, text4) → t2
  11. If(b ≟ 1, text6, text6) → t4
  12. Random(1, 4) → j
  13. If(b ≟ 1, text5, text3) → t3
  14. If(m ≟ 1, "A", If[m ≟ 2, "B", If[m ≟ 3, "C", "D"]]) → text26
  15. If(j ≟ 1, "A", If[j ≟ 2, "B", If[j ≟ 3, "C", "D"]]) → text27
  16. Asymptote(c) → f_1, g_1
  17. Asymptote(d) → h_1, i_1
  18. Line(F, xAxis) → j_1
  19. Line(G, j_1) → k_1
  20. Intersect(j_1, h_1) → J
  21. Intersect(i_1, j_1) → K
  22. Intersect(k_1, xAxis) → L
  23. Intersect(i_1, k_1) → M
  24. Intersect(h_1, k_1) → N
  25. Segment(J, M) → l_1
  26. Segment(J, K) → m_1
  27. Segment(K, N) → n_1
  28. Segment(N, M) → p_1
  29. Asymptote(c) → q_1, r_1
  30. Line(C, yAxis) → s_1
  31. Line(B, yAxis) → t_1
  32. Intersect(r_1, s_1) → O
  33. Intersect(t_1, q_1) → P
  34. Intersect(q_1, s_1) → Q
  35. Intersect(t_1, r_1) → R
  36. Segment(O, Q) → a_1
  37. Segment(Q, R) → b_1
  38. Segment(R, P) → c_1
  39. Segment(P, O) → d_1