IMO 1969 LL BEL1

A parabola P1 with equation x2 −2py = 0 and parabola P2

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IMO 1969 LL BEL1

Origin: BEL

Problem

A parabola P1 with equation x2 −2py = 0 and parabola P2 with equation x2 + 2py = 0, p > 0, are given. A line t is tangent to P2. Find the locus of pole M of the line t with respect to P1.