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Hyperbola x^2-y^2=1 and Translations

Hyperbola x^2-y^2=1 and Translations
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2013-06-28 11:16
FunctionCoordinate Geometry
This example demonstrates the basic hyperbola relation x^2-y^2=1 and its translations. Key math concepts include hyperbola equation, translation transformation, and coordinate geometry. It uses GeoGebra commands like SecondAxis, FirstAxis, Intersect, Segment for construction. Suitable for high school students learning hyperbola properties and transformations.

GeoGebra Commands & Parameters

  1. SecondAxis(c) → d
  2. FirstAxis(c) → e
  3. Intersect(e, d) → A
  4. Intersect(c, f) → D, E
  5. Segment(A, E) → xdist
  6. Segment(D, A) → i

AI Drawing Prompt Reference

Draw a hyperbola x²-y²=1 and its translations, start by plotting the basic hyperbola, then mark the coordinate axes, find the intersection points between the axes and the hyperbola, connect these points to form translated hyperbolas, and use line segments to show the translation distance and transformation relationships.
The prompt above was compiled from the original drawing commands and is for reference only.