The equations of three of the graphs in this family of rectangular hyperbolae are:

xy = 1

(x - 3) y = 1

and

xy = - 1 .

Find the equations of the other graphs in this illustration.

Now draw your own family of hyperbolae by taking different values of the constants $a$ and $b$ in the equation

$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 .$

You may like to use a graphing software package such as Graphmatica which is available as a free download from http://www8.pair.com/ksoft