Rectangular Hyperbola Intercept Property Demo

Rectangular Hyperbola Intercept Property Demo
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2015-08-01 11:10
This example demonstrates the property that the length of the intercept cut off a tangent by the asymptotes of a rectangular hyperbola equals twice the parameter t. It involves core concepts like hyperbola, asymptotes, tangent, intercepts, and parameter equations. GeoGebra commands and objects used include Point, Tangent, Intersect, Segment, and Distance for construction. Suitable for high school and above mathematics learners to understand geometric properties and applications of parameter equations.

GeoGebra Commands & Parameters

  1. Point(f) → P
  2. Tangent(P, f) → b
  3. Intersect(b, yAxis) → Y
  4. Intersect(b, xAxis) → X
  5. Intersect(yAxis, xAxis) → O
  6. Segment(Y, X) → d
  7. Segment(O, P) → e
  8. Distance(Y, X) → distanceYX
  9. Distance(O, P) → distancePO