IrMO 1989 Problem 6

Suppose $L$ is a fixed line, and $A$ is a fixed point not on $L$ . Let $k$ be a fixed nonzero real number. For $P$ a point on $L$ , let $Q$ be a point on the line $AP$ with $|AP|\cdot |AQ|=k^2$ . Determine the locus of $Q$ as $P$ varies along the line $L$ .