Syntractrix

A syntractrix is a curve of the form

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

The syntractrix for [math]\displaystyle{ a=0.5 }[/math] and [math]\displaystyle{ b=1. }[/math]

The syntractrix for [math]\displaystyle{ a=1.5 }[/math] and [math]\displaystyle{ b=1. }[/math]

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.