The following discussion may be of interest on account of the way in which it leads to the axial and focal properties. I. Let the locus of a point P such that A(CDEP) = B(CDEP), where A, B, C, D, E are fixed points, be called the conic (AB, CDE). Then it is clear that permuting A, B or C, D, E does not affect the conic, and that the conic passes through C, D, E , and also through A, B . (Give BP the four positions BC, BD, BE, BA and then give AP the position AB .)