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

x²
a²
- y²
b²
= 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