Syntractrix

A syntractrix is a curve of the form

:$x+\backslash sqrt\{b^2-y^2\}=\; a\; \backslash ln\; \backslash frac\{b+\backslash sqrt\{b^2-y^2\}\}\{y\}.$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]

File:Syntractrix a=0.5 b=1.png

File:Syntractrix a=1.5 b=1.png

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.Dionysius Lardner, A system of algebraic geometry 1823, p. 261–263 [https://books.google.com/books?id=0zUDAAAAQAAJ&q=Syntractrix]