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Animating the Ellipse

Animating the Ellipse
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2016-12-10 05:36
Parametric EquationGeometric ConstructionSlider Animation
This example demonstrates the animation of an ellipse. Key mathematical concepts include the geometric properties and parametric equations of an ellipse. Using GeoGebra commands like CurveCartesian, users can dynamically observe the formation of the ellipse.

GeoGebra Commands & Parameters

  1. Plane(A, B, C) → c
  2. CurveCartesian(sqrt((40 * t) - (3 * t^(2)) - 100), 10 - (2 * t), t, t, 0, 10) → d
  3. CurveCartesian((-sqrt(((-1 / 2 * t) + f)^(2) - t^(2))), t, (-1 / 2 * t) + f, t, -10, 10) → j
  4. CurveCartesian((-sqrt(((-1 / 2 * t) + f)^(2) - t^(2))), t, (-1 / 2 * t) + f, t, -10, 10) → k
  5. CurveCartesian((-sqrt((40 * t) - (3 * t^(2)) - 100)), 10 - (2 * t), t, t, 0, 15) → e
  6. CurveCartesian(sqrt(((-1 / 2 * t) + f)^(2) - t^(2)), t, (-1 / 2 * t) + f, t, -25, 25) → h
  7. CurveCartesian((-sqrt(((-1 / 2 * t) + f)^(2) - t^(2))), t, (-1 / 2 * t) + f, t, -25, 25) → i