MacLaurin's Construction of Conics

Let ABC be a variable triangle which is such that the vertices B and C respectively move on two given lines l and m, and the sides BC, CA, and AB respectively pass through given points U, V, and W. Then the locus of the vertex A is a conic. If points U, V, W, are collinear then the locus degenerates into a straight line concurrent with l and m.

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