Syntractrix

A syntractrix is a curve of the form

$x%2B\sqrt{b^2-y^2}= a \ln \frac{b%2B\sqrt{b^2-y^2}}{y}.$

References

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. [1]