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Ellipses Translation

Ellipses Translation
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2017-04-30 20:54
Coordinate GeometryTransformation
In collections Conics Investigation
This example demonstrates the translation of ellipses. Key mathematical concepts include the definition of an ellipse, translation transformations, and their effects on the geometric properties of the ellipse. By adjusting parameters a, b, h, and k, the position of the ellipse can be observed. The construction uses GeoGebra commands such as points, lines, and loci.

GeoGebra Commands & Parameters

  1. Numeric a(2.4)
  2. Numeric b(3.15)
  3. Numeric h(0)
  4. Numeric k(0)
  5. (h, k)
  6. sqrt(a^(2) - b^(2))
  7. (h + c, k)
  8. (h - c, k)
  9. sqrt(b^(2) - a^(2))
  10. (h, k + d)
  11. (h, k - d)
  12. (h, k + b)
  13. (h + a, k)
  14. (h, k - b)
  15. (h - a, k)
  16. (x - h)^(2) / a^(2) + (y - k)^(2) / b^(2) = 1
  17. (x - 3)^(2) / 2^(2) + (y - 4)^(2) / 3^(2) = 1
  18. Boolean boo1(false)
  19. Boolean boo2(false)
  20. (x + 5)^(2) / 5^(2) + (y - 3)^(2) / 2^(2) = 1