You are asked to sketch the graphs in this family not by plotting and joining points but by considering the general features of the graph of the rectangular hyperbola xy=1 and of transformations of this graph.

When you make your own pattern of hyperbolae using the equation

x²
a²
- y²
b²
= 1

you might like to try making the same transformations as those used in the example Ellipses where the family of equations is given by

x²
a²
+ y²
b²
= 1.

See the challenge Ellipses here.