A pursuit curve is the trajectory which hunter X follows to catch its prey A. Both X and A are assumed to be mobile points where the velocity of X is higher than that of A. A pursuit curve is characterized by the following geometrical property: the straight line tangent to this curve, at the point where hunter X is located at any time 0 ⩾ t, passes through the point where prey A lies. In this work, the analytical expression of the time used by X in capturing A is deduced, the contour corresponding to the unit ball in terms of travel time is analysed and a location problem related to the Weber problem is formulated. Namely, we locate a single hunter on the plane which minimizes the weighted sum of capture time with respect to a finite set of prey.
