This document discusses loci and how to write equations representing loci given certain conditions. It begins by defining a locus as a set of points traced by a moving point based on a specific rule or condition. Examples are then given of writing equations for loci of points equidistant from two given points, finding the midpoint, or a fixed distance from a single point. The key is setting up equations relating the distances defined by the condition and solving for the relationship between x and y coordinates.