This is a typical square hyperbola. It's obvious that, the arms of the graphs grow closer and closer to the co-ordinate axes which are at right angles to each other, which is what makes this a square hyperbola. If the hyperbola were rotated through some angle the arms would still be approach two lines at right angles and therefore the hyperbola would still be a square one. The equation of this particular hyperbola is x y = 5 xy=5 .

A Hyperbola which has Its asymptotes at a right angle is called a rectangular Hyperbola. The equation of rectangular hyperbola referred to its transverse and conjugate axes as axes of coordinates is, therefore, x2 – y2 = a2. The eccentricity of a rectangular hyperbola = √2.