Why do this problem?

The problem gives practice in the usual techniques for cuve sketching (considering symmetry, finding turning points, looking for asymptotes). It also introduces the idea of a family of curves.

Possible approach

Suggest different members of the class sketch the different graphs (for $a=1$, $2$ and $3$). Have a class discussion about the results they find.

Key question

Will the graphs have a similar shape for all values of $a$?

What about negative values of $a$?

Possible extension

If the class can differentiate simple functions defined parametrically or implicitly then they could also try: Squareness and Folium of Descartes .