Bisoptic curves of hyperbolas |
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Authors: | Thierry Dana-Picard Giora Mann Nurit Zehavi |
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Affiliation: | 1. Department of Mathematics, Jerusalem College of Technology, Jerusalem, Israelndp@jct.ac.il;3. Beit Chanan, 76868 Rehovot, Israel;4. Department of Science Teaching, Weizmann Institute of Science, Rehovot,?Israel |
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Abstract: | Given a hyperbola, we study its bisoptic curves, i.e. the geometric locus of points through which passes a pair of tangents making a fixed angle θ or 180° ? θ. This question has been addressed in a previous paper for parabolas and for ellipses, showing hyperbolas and spiric curves, respectively. Here the requested geometric locus can be empty. If not, it is a punctured spiric curve, and two cases occur: the curve can have either one loop or two loops. Finally, we reconstruct explicitly the spiric curve as the intersection of a plane with a self-intersecting torus. |
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Keywords: | bisoptic curves conic sections toric sections |
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