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GeoGebraGeoGebra Classroom

Ellipse, Hyperbola and Circle as Envelopes

In the app below you can explore how a single construction can create ellipses, hyperbolas and circles. Place point where you want and start the animation, or move point along the circle of center and radius . The position of relative to the circle determines the conic envelope:
  • inside ellipse with foci , and major semi-axis length
  • coinciding with circle with center and radius
  • outside hyperbola with foci and semi-axis length