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