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AQ_|_QP , A(1,0), L lies on line y = kx

Source: 1975 Swedish Mathematical Competition p1

March 26, 2021
analytic geometryalgebra

Problem Statement

AA is the point (1,0)(1,0), LL is the line y=kxy = kx (where k>0k > 0). For which points P(t,0)P(t,0) can we find a point QQ on LL such that AQAQ and QPQP are perpendicular?
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