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Locus of Q as P Varies Along L

Source: 1989 IrMO Paper 2 Problem 1

September 29, 2017
geometry

Problem Statement

Suppose LL is a fixed line, and AA is a fixed point not on LL. Let kk be a fixed nonzero real number. For PP a point on LL, let QQ be a point on the line APAP with ∣AP∣⋅∣AQ∣=k2|AP|\cdot |AQ|=k^2. Determine the locus of QQ as PP varies along the line LL.
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