If the asymptotes be perpendicular, or, in other words, the principal axes be equal, the curve is called the rectangular hyperbola.
We may observe that the asymptotes intersect this circle in the same points as the directrices.
If the tangent at P meets the asymptotes in R, R', then CR.CR' = CS 2.
Referred to the asymptotes as axes the general equation becomes xy 2 obviously the axes are oblique in the general hyperbola and rectangular in the rectangular hyperbola.
The isothermals are approximately equilateral hyperbolas (pv= constant), with the axes of p and v for asymptotes, for a gas or unsaturated vapour, but coincide with the isopiestics for a saturated vapour in presence of its liquid.