Describing circles as a indexed family of sets. I have the following task:
"Describe the following as an indexed family of sets. Here $\Pi$ denotes the coordinatized xy-plane: The family of all circles in $\Pi$ of radius 1."
the general equation would be of the form:
$$ (x-a)^2 + (y -b)^2 = 1$$
or one of the other equivalent equations. I am unsure  how one is able to determine the index given that  the centre would be depend on two variables 

Sounds like somethin like this:
$$
\mathcal{A} = \{ A_u \,\left|\, u \in \Pi \right. \} \quad 
\mbox{where} \quad 
A_u = \left\{ v \in \Pi \left| \, ||v - u|| = 1 \right. \right\}
$$
