Pursuit Curve

If $A$ moves along a known curve, then $P$ describes a pursuit curve if $P$ is always directed toward $A$ and $A$ and $P$ move with uniform velocities. These were considered in general by the French scientist Pierre Bouguer in 1732. The case restricting $A$ to a straight line was studied by Arthur Bernhart (MacTutor Archive). It has Cartesian Coordinates equation

$$y = cx-\ln x.$$

See also Apollonius Pursuit Problem, Mice Problem

References

Bernhart, A. ``Curves of Pursuit.'' Scripta Math. 20, 125-141, 1954.

Bernhart, A. ``Curves of Pursuit-II.'' Scripta Math. 23, 49-65, 1957.

Bernhart, A. ``Polygons of Pursuit.'' Scripta Math. 24, 23-50, 1959.

Bernhart, A. ``Curves of General Pursuit.'' Scripta Math. 24, 189-206, 1959.

MacTutor History of Mathematics Archive. ``Pursuit Curve.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Pursuit.html.

Yates, R. C. ``Pursuit Curve.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 170-171, 1952.