Right Hyperbola

A Hyperbola for which the Asymptotes are Perpendicular. This occurs when the Semimajor and Semiminor Axes are equal. Taking $a=b$ in the equation of a Hyperbola with Semimajor Axis parallel to the x-Axis and Semiminor Axis parallel to the y-Axis (i.e., vertical Directrix),

$${(x-x_0)^2\over a^2} - {(y-y_0)^2\over b^2} = 1$$

therefore gives

$$(x-x_0)^2-(y-y_0)^2=a^2.$$

A special type of right hyperbola is the so-called Rectangular Hyperbola, which has equation $xy=ab$.

See also Hyperbola, Rectangular Hyperbola