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Ellipse Equation Construction Practice

Ellipse Equation Construction Practice
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2018-11-27 21:08
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to dynamically construct an ellipse equation through interactive manipulation. It involves core mathematical concepts such as the definition of an ellipse, standard and parametric equations, and coordinate geometry. GeoGebra commands and objects like RandomElement, Random, If, Element, and Ellipse are used, with sliders to dynamically adjust ellipse parameters. Suitable for high school mathematics teaching to help students understand the geometric meaning of ellipse equations and the effect of parameter changes on the graph.

GeoGebra Commands & Parameters

  1. RandomElement(L_4) → s
  2. Random(-9, 9) → k1
  3. Random(-9, 9) → h
  4. If(k1 ≟ 0 ∧ h ≟ 0, k1 + 1, k1) → k
  5. Random(1, 6) → n
  6. Element(L_3, n) → a
  7. Element(L_2, n) → b
  8. Element(L_1, n) → c
  9. If(k > 0, "(" + "y-" + k + ")²", If[k < 0, "(" + "y+" + (((-k) * ")²")), "y²"]) → text2
  10. If(h > 0, "(" + "x-" + h + ")²", If[h < 0, "(" + "x+" + (((-h) * ")²")), "x²"]) → text1
  11. If(h > 0, "(" + "x+" + h + ")²", If[h < 0, "(" + "x-" + (((-h) * ")²")), "x²"]) → text3
  12. If(k > 0, "(" + "y+" + k + ")²", If[k < 0, "(" + "y-" + (((-k) * ")²")), "y²"]) → text4
  13. If(h > 0, "-" + (abs(((2 * h) * b2))) + "x", If[h < 0, "+" + (abs(((2 * h) * b2))) + "x", ""]) → text10
  14. If(d < 0, "-" + (abs((-d))), If[d > 0, "+" + d, ""]) → text12
  15. If(k > 0, "-" + (abs(((2 * k) * a2))) + "y", If[k < 0, "+" + (abs(((2 * k) * a2))) + "y", ""]) → text11
  16. If(h > 0, "-" + (abs(((2 * h) * a2))) + "x", If[h < 0, "+" + (abs(((2 * h) * a2))) + "x", ""]) → text15
  17. If(k > 0, "-" + (abs(((2 * k) * b2))) + "y", If[k < 0, "+" + (abs(((2 * k) * b2))) + "y", ""]) → text16
  18. If(e < 0, "-" + (abs((-e))), If[e > 0, "+" + e, ""]) → text17
  19. If(e1 < 0, "-" + (abs((-e1))), If[e1 > 0, "+" + e1, ""]) → text171
  20. If(d1 < 0, "-" + (abs((-d1))), If[d1 > 0, "+" + d1, ""]) → text121
  21. If(n_1 ≟ 1, Random[1, 2], If[n_1 ≟ 2, Random[3, 4], Random[1, 4]]) → f
  22. If(f ≟ 1, t01, If[f ≟ 2, t21, If[f ≟ 3, t11, t31]]) → t001
  23. If(f ≟ 1, t02, If[f ≟ 2, t22, If[f ≟ 3, t12, t32]]) → t002
  24. If(f ≟ 1, t03, If[f ≟ 2, t23, If[f ≟ 3, t13, t33]]) → t003
  25. If(f ≟ 1, t04, If[f ≟ 2, t24, If[f ≟ 3, t14, t34]]) → t004
  26. Random(1, 4) → i
  27. Ellipse(FX1, FX2, a) → p
  28. Ellipse(FY1, FY2, a) → q
  29. If(g ≟ 1, "A", If[g ≟ 2, "B", If[g ≟ 3, "C", "D"]]) → text44
  30. If(i ≟ 1, "A", If[i ≟ 2, "B", If[i ≟ 3, "C", "D"]]) → text45
  31. If(n_1 ≟ 1, "สมการมาตรฐาน", If[n_1 ≟ 2, "สมการทั่วไป", "แบบระคน"]) → text48

AI Drawing Prompt Reference

Draw a dynamic ellipse with adjustable parameters via sliders, showing both standard and parametric equations. The ellipse's center is in the coordinate system, with variable major and minor axes. Dynamically display the parametric and standard equations of the ellipse, and label the foci and vertices.
The prompt above was compiled from the original drawing commands and is for reference only.