IMO 1965 Problem 5

Consider $\triangle OAB$ with acute angle $AOB$ . Thorugh a point $M \neq O$ perpendiculars are drawn to $OA$ and $OB$ , the feet of which are $P$ and $Q$ respectively. The point of intersection of the altitudes of $\triangle OPQ$ is $H$ . What is the locus of $H$ if $M$ is permitted to range over

a) the side $AB$ ;

b) the interior of $\triangle OAB$ .