rectangular hyperbola

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A hyperbola whose asymptotes are perpendicular. With the origin at the centre and the coordinate x-axis along the transverse axis, it has equation x2y2=a2. 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=c2. For example, y=1/x is a rectangular hyperbola. For xy=c2, 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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