1. Nowadays the beginning of conics is a blend of pure and coordinate geometry, but the starting point is generally the focus-directrix definition. From this the standard equations and properties are deduced, but a good deal of time is taken before some of the more powerful methods can be applied.

The object here is to indicate compact proofs of some well-known results, and to obtain, at an early stage, such results as Newton’s Theorem and the cross-ratio property from the focus-directrix definition.