Ellipse, Hyperbola and Circle as Envelopes
- Author:
- Simona Riva
- Topic:
- Circle, Ellipse, Hyperbola, Straight Lines
In the following app you can explore an "all-in-one" construction of the envelopes of ellipses, hyperbolas and circles.
Set the position of the focus by dragging it, then start the animation, or move point along the circle, that has center at and radius .
The position of with respect to the circle determines the generated envelope as follows:
- inside the circle → ellipse with foci , and semi-major axis
- coincident with → circle with center and radius
- outside the circle → hyperbola with foci , e semi-major axis