Rectangular hyperbola

When the two semi-axes are equal ($a=b$) the hyperbola is said to be rectangular: its asymptotes become the bisectors of the quadrants, perpendicular to each other. If one then rotates the frame by $45°$ until it coincides with the asymptotes, the equation takes the very simple form $xy=k$: it is the inverse proportionality already met in Year One.

• Definition of the rectangular hyperbola
• Rectangular hyperbola referred to its asymptotes