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Ellipse by Chris Coffey

Ellipse by Chris Coffey
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2019-04-01 01:55
Coordinate GeometryGeometric Construction
This example demonstrates the construction of an ellipse. Key mathematical concepts include the definition of an ellipse, foci, and center. Using GeoGebra commands like a, b, h, k, c, d, the parameters of the ellipse can be dynamically adjusted. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Numeric a(1)
  2. Numeric b(1)
  3. Numeric h(0)
  4. Numeric k(0)
  5. (x - h)^(2) / a^(2) + (y - k)^(2) / b^(2) = 1
  6. (x - h)^(2) / b^(2) + (y - k)^(2) / a^(2) = 1
  7. a^(2) - b^(2)
  8. (h + sqrt(c_{1}), k)
  9. (h - sqrt(c_{1}), k)
  10. b^(2) - a^(2)
  11. (h, k + sqrt(c_{2}))
  12. (h, k - sqrt(c_{2}))
  13. (h, k)

AI Drawing Prompt Reference

Draw an ellipse with adjustable semi-major and semi-minor axes, centered at a point with given coordinates. Plot two ellipses: one with the major axis horizontal and one with the major axis vertical. Compute the difference of the squares of the two axes to determine the foci positions: for the horizontal ellipse, place foci left and right of the center; for the vertical ellipse, place foci above and below the center. Mark the center point. The final figure includes both ellipses, their foci, and the center, all in the same coordinate system.
The prompt above was compiled from the original drawing commands and is for reference only.