In this paper we describe a novel approach to reactive tracking of moving targets with a pan-tilt-zoom camera. The approach uses an extended Kalman filter to jointly track the object position in the real world, its velocity in 3D and the camera intrinsics, in addition to the rate of change of these parameters. The filter outputs are used as inputs to PID controllers which continuously adjust the camera motion in order to reactively track the object at a constant image velocity while simultaneously maintaining a desirable target scale in the image plane. We provide experimental results on simulated and real tracking sequences to show how our tracker is able to accurately estimate both 3D object position and camera intrinsics with very high precision over a wide range of focal lengths.