A hyperbola is said to be a rectangular hyperbola if its asymptotes are at right angles.

The angle between the asymptotes is given by 2 tan^{−1} (b/a).

b/a = tan 45° = 1

a = b

The equation of rectangular hyperbola is

x^{2} − y^{2} = a^{2}

The combined equation of the asymptotes is x^{2} − y^{2} = 0. The separate equations are x − y = 0 and x + y = 0. i.e., x = y and x = −y. The transverse axis is y = 0, conjugate axis is x = 0.