
06361434
j
2014f.00653
DanaPicard, Thierry
Mann, Giora
Zehavi, Nurit
Bisoptic curves of hyperbolas.
Int. J. Math. Educ. Sci. Technol. 45, No. 5, 762781 (2014).
2014
Taylor \& Francis, Abingdon, Oxfordshire
EN
G70
I90
bisoptic curves
conic sections
toric sections
doi:10.1080/0020739X.2013.877608
Summary: 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 $\theta$ or $180^{\circ}  \theta$. 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 selfintersecting torus.