Question 58
Given two parallel lines $r, s$ and two points $P, Q$ with $P \in r$ and $Q \in s$ in the plane, consider pairs of circles $\left(C_{P}, C_{Q}\right)$, the first tangent to $r$ in $P$ and the second tangent to $s$ in $Q$, which are also externally tangent to each other, at a point we call $T$. Determine the locus of these points $T$ as all possible pairs of circles vary.