There are no definite references - but I have only been able to trace back to Pappus and possibly Aristaeus, a contemporary of Euclid. I'm trying to piece together the path to our current taught definitions of conic sections in terms of foci and directrix.
Here's the best reference/citation I have found so far:
Heath makes a guess at the possible contents of the Solid Loci and writes [3]:-
A very large portion of the standard properties of conics admit of being stated in the form of locus theorems ... But it may be assumed that Aristaeus's work was not merely a collection of the ordinary propositions transformed in this way; it would deal with new locus theorems not implied in the fundamental definitions and properties of the conics, such as ... the theorems of the three- and four-line locus. But one (to us) ordinary property, the focus directrix property, was, as it seems to me, in all probability included.
This implies that they were probably known to Aristaeus and since there was a tendency to define stuff with reference to loci of points, Aristaeus found a way to define conics that way. But, he had to introduce a notion of a directrix when talking about parabolas and hyperbolas.
By what references did we (in modern times) get the idea of the foci and directrix? Or was it rediscovered? Any sources/references?