Locating parameters of interest in a conic section

Extract

In an interesting Note [1] a method for constructing the directrices of a conic section using simple tools, viz. a pencil, a pair of compasses and a straight edge, was presented and it was wondered if the method might have been known before. From earlier days at school this author was aware that for a specific conic section (parabola, ellipse or hyperbola) displayed without reference on a piece of paper it was possible to determine not just the directrices but also the focal points and the usual axis set, again using just the simple tools. Others might also be aware of these facts, but if they are not so well known it might be of interest to present an argument in recipe format that will enable readers to appreciate a route to fathom the business, although there might well be other paths leading also to the same end-result, depending on the starting point.