Here's a diagram of the Conchoid of Nicomedes. This can be used for numerous things such as trisecting angles, and cube duplication. A line l, a point O that’s not on the line, and a distance k. There is going to be a line m passing through O and any point P on line l. There are two points, Q1 and Q2, which are going to be in line m such that the distance between Q1 and P equals the distance between Q2 and p which also equals k. The locus of Q1 and Q2 as P varies on the line l, this locus is the Conchoids of Nicomedes. In other words, the Conchoids of Nicomedes is the locus of points that are a certain distance away from a line measured along a line from the focus point. The formula for this in Cartesian coordinates is (a – b – x)(a + b –x)x^2 + (a – x)^2 * y^2 = 0 .