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Locus of pole of a line with respect to parabola.

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September 29, 2010
conicsparabolageometryLocusLocus problemsIMO ShortlistIMO Longlist

Problem Statement

(BEL1)(BEL 1) A parabola P1P_1 with equation x2−2py=0x^2 - 2py = 0 and parabola P2P_2 with equation x2+2py=0,p>0x^2 + 2py = 0, p > 0, are given. A line tt is tangent to P2.P_2. Find the locus of pole MM of the line tt with respect to P1.P_1.
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