Circle and Hyperbola As Lighthouse Curves
A Mathematical Droodle

Two lines rotate with constant angular velocities around two points in a plane. (An apt metaphore of two lighthouses was invented by R. K. Guy of the University of Calgary.) The point illuminated by two beams traces a curve. What is it?

Equal angular velocities:


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Opposite angular velocities


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Explanation

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Copyright © 1996-2017 Alexander Bogomolny

For circles, the explanation is based on the equality of the inscribed angles subtended by the same arc.

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Copyright © 1996-2017 Alexander Bogomolny

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