## Quick Reference

A hyperbola whose asymptotes are perpendicular. With the origin at the centre and the coordinate *x*-axis along the transverse axis, it has equation *x*^{2}−*y*^{2}=*a*^{2}. Instead, the coordinate axes can be taken along the asymptotes in such a way that the two branches of the hyperbola are in the first and third quadrants. This coordinate system can be obtained from the other by a rotation of axes. The rectangular hyperbola then has equation of the form *xy*=*c*^{2}. For example, *y*=1/*x* is a rectangular hyperbola. For *xy*=*c*^{2}, it is customary to take *c*>0 and to use, as parametric equations, *x*=*ct*, *y*=*c*/*t* (*t* ≠ 0).

*Subjects:*
Chemistry — Mathematics.

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