IMO 1969 - Longlist Problems Question 1

(BEL 1) A parabola $P_1$ with equation $x^2-2py=0$ and parabola $P_2$ with equation $x^2+2py=0$, $p>0$, are given. A line $t$ is tangent to $P_2$. Find the locus of pole $M$ of the line $t$ with respect to $P_1$.