Ononot — Consider the family of circles x^2 + y^2 - 2x - 4y + 5 + \la

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Coordinate Geometryhard

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Consider the family of circles $x^2 + y^2 - 2x - 4y + 5 + \lambda(x - 2y + 1) = 0$ . What is the locus of the centers of these circles?