IMO 1989 LL INA44

Let A and B be fixed distinct points on the X axis, none of

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IMO 1989 LL INA44

Origin: INA

Problem

Let A and B be fixed distinct points on the X axis, none of which coincides with the origin O(0, 0), and let C be a point on the Y axis of an orthogonal Cartesian coordinate system. Let g be a line through the origin O(0, 0) and perpendicular to the line AC. Find the locus of the point of intersection of the lines g and BC as C varies along the Y axis. (Give an equation and a description of the locus.)