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Parametric Ellipse Equation

Parametric Ellipse Equation
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2018-01-29 23:13
Coordinate GeometryParametric EquationGeometric Construction
This example demonstrates the parametric equation of an ellipse, involving the parametric representation of ellipses. Using GeoGebra commands such as Intersect, Rotate, Angle, etc., it dynamically illustrates the geometric properties of ellipses. Suitable for high school math education, helping students understand the parametric equation and geometric meaning of ellipses.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Intersect(d, xAxis) → A'_2, A_2
  3. Rotate(A_2, α, O) → A'
  4. Angle(A_2, O, A') → φ
  5. Ray(O, A') → e
  6. Intersect(c, e) → B',
  7. OrthogonalLine(A', xAxis) → f
  8. OrthogonalLine(B', f) → g
  9. Intersect(f, g) → E
  10. Segment(A', E) → h
  11. Segment(B', E) → i
  12. If(j, 1, 0) → speed
  13. Intersect(f, xAxis) → Γ
  14. Intersect(g, yAxis) → Δ
  15. Segment(O, Γ) → k
  16. Segment(Δ, O) → l
  17. Segment(A', Γ) → m
  18. Segment(O, A') → n
  19. Intersect(c, yAxis) → B'_1, B_2
  20. Segment(B', Δ) → p
  21. Angle(Δ, B', O) → γ

AI Drawing Prompt Reference

Draw an ellipse to demonstrate its parametric equation. Start by plotting the coordinate axes and finding their intersection as the origin. Determine the major and minor axes of the ellipse, rotating a point on the major axis to locate a point on the minor axis. Then, use these points to draw auxiliary lines and find their intersection. Finally, connect these key points with line segments to form the ellipse's outline, dynamically illustrating the geometric meaning of its parametric equation.
The prompt above was compiled from the original drawing commands and is for reference only.