Syntractrix

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]

A syntractrix is a curve of the form

${\displaystyle x+{\sqrt {b^{2}-y^{2}}}=a\ln {\frac {b+{\sqrt {b^{2}-y^{2}}}}{y}}.}$[1]

The syntractrix for ${\displaystyle a=0.5}$ and ${\displaystyle b=1.}$

The syntractrix for ${\displaystyle a=1.5}$ and ${\displaystyle b=1.}$

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.
2. Dionysius Lardner, A system of algebraic geometry 1823, p. 261–263