Syntractrix

A syntractrix is a curve of the form x + b 2 − y 2 = a ln ⁡ b + b 2 − y 2 y . {\displaystyle x+{\sqrt {b^{2}-y^{2}}}=a\ln {\frac {b+{\sqrt {b^{2}-y^{2}}}}{y}}.} 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.

A syntractrix is a curve of the form

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

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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]

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