Pursuit Curve
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 in1732. The case restricting to a straight line was studied by Arthur Bernhart (MacTutor Archive). It hasCartesian 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.
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