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Conic Sections with Translations Demo

Conic Sections with Translations Demo
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2015-09-09 00:38
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the translation transformations of conic sections (circle, ellipse, hyperbola, parabola) in the coordinate system. It involves core mathematical concepts such as the definition of conic sections, standard equations, translation transformations, and analytical geometry. The construction uses GeoGebra commands and objects like a, b, h, k for parameters, Conic for the conic sections, c, f, r, p, q for auxiliary calculations and drawing, text1 to text5 for annotations, and g, d, e for auxiliary graphics. It is suitable for high school students to learn and understand the properties and transformations of conic sections.

GeoGebra Commands & Parameters

  1. Numeric a(1.0)
  2. Numeric b(1.0)
  3. Numeric h(0.0)
  4. Numeric k(0.0)
  5. Numeric Conic(1.0)
  6. (x - h)^(2) / a^(2) + (y - k)^(2) / b^(2) = 1
  7. (x - h)^(2) / a^(2) - (y - k)^(2) / b^(2) = 1
  8. Numeric r(1.0)
  9. (x - h)^(2) + (y - k)^(2) = r^(2)
  10. y = (x - h)^(2) + k
  11. (y - k)^(2) / b^(2) - (x - h)^(2) / a^(2) = 1
  12. y = (b / a * (x - h)) + k
  13. y = ((-(b / a)) * (x - h)) + k

AI Drawing Prompt Reference

Draw a unit circle centered at the origin, then translate it to create an ellipse and a hyperbola. Finally, draw a parabola with its vertex at the origin and show its focus and directrix.
The prompt above was compiled from the original drawing commands and is for reference only.