Juan Rodriguez, Paula Manuel, and Paulo Simiao, A conic associated with Euler lines,
Forum Geometricorum, 6 (2006) 17--23.

Abstract: We study the locus of a point C for which the Euler line of  triangle ABC with given A and B has a given slope m. This is a conic through A and B, and with center (if it exists) at the midpoint of AB. The main properties of such an Euler conic are described. We also give a construction of a point C for which triangle ABC, with A and B fixed, has a  prescribed Euler line.

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