A conic asssociated with Euler Lines - Semião, Paulo (2014)
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.