Syntractrix Explained

A syntractrix is a curve of the form

x + \sqrt{b ^{2-y} ^{2}=} a ln (b + \sqrt{b ^{2-y} ^{2})/() }.^[1]

It is the locus of a point on the tangent of a tractrix at a constant distance from the point of tangency, as the point of tangency is moved along the curve.^[2]

Notes and References

1. George Salmon (1879). A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on Conic Sections. Published by Hodges, Foster, and Figgis. Page 290. https://books.google.com/books?id=Vv43AAAAMAAJ&pg=PA289
2. [Dionysius Lardner]