Tractorix

Japanese: tractrix

…The curve that is represented by the graph of the hyperbolic cosine function is called a catenary, or a catenary. It is the figure drawn by the focus of the parabola y = x ² /(4 a ) when it rolls along the x -axis without slipping, and it is also the figure drawn by the center of curvature of the curve (called the tractrix) drawn by a weight at A(0, a ) when it is pulled along the x- axis by a string of length a . When a string of uniform density is supported at both ends and suspended in a field of gravity, the string takes on the shape of this curve. …

From [Curve]

...The equation of the involute of this curve at A is. This curve is called a tractrix. If the intersection point of the tangent at point P on this curve and the x- axis is Q, the length of PQ is always a (Figure 20). ...

*Some of the terminology explanations that mention "tractrix" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…双曲線余弦関数のグラフで表される曲線をカテナリー，または懸垂線という。これは放物線y＝x²/(4a)がx軸上をすべらずに転がるときにその放物線の焦点の描く図形であり，また，A(0,a)にあるおもりを長さaの糸でx軸上に引いていくときにそのおもりの描く曲線(これをトラクトリックスtractrixという)の曲率中心の描く図形でもある。密度一様な糸の両端を支えて重力の場につり下げるときの糸はこの曲線の形状をとる。…