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Transformations of Ellipse

Transformations of Ellipse
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2022-12-16 19:05
Coordinate GeometryTransformationGeometric Construction
This example demonstrates transformations of an ellipse, including translation and rotation. Key mathematical concepts include geometric transformations and coordinate geometry. By adjusting parameters, you can observe how the ellipse changes under different transformations. Mainly uses GeoGebra objects a, b, h, k, A for construction.

GeoGebra Commands & Parameters

  1. Numeric a(4.1)
  2. Numeric b(6.2)
  3. Numeric h(-2.2)
  4. Numeric k(-0.5)
  5. Angle A(1.413716694115407)
  6. (((x - h) * cos(A)) + ((y - k) * sin(A)))^(2) / a^(2) + (((x - h) * sin(A)) - ((y - k) * cos(A)))^(2) / b^(2) = 1

AI Drawing Prompt Reference

Draw an ellipse centered at (-2.2, -0.5) with a major axis length of 4.1 and a minor axis length of 6.2, then rotate it by an angle of 1.413716694115407 to demonstrate translation and rotation transformations.
The prompt above was compiled from the original drawing commands and is for reference only.