Syntractrix

A syntractrix is a curve of the form

x+\sqrt{b^2-y^2}= a \ln \frac{b+\sqrt{b^2-y^2}}{y}.

^[1]

The syntractrix for

a=0.5

and

b=1.

The syntractrix for

a=1.5

and

b=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]

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

[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. [1]

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

[1]

[2]