One of the major challenges slowing down the use of unmanned aerial vehicles (UAVs) as aerial base stations (ABSs) is the limited onboard power supply, which reduces the flight time of a UAV. Using a tether to provide UAVs with power can be considered a reasonable compromise that will enhance the flight time while limiting the mobility of the UAV. In this article, we propose a system where ABSs are deployed at the centers of user hotspots to offload the traffic and assist terrestrial base stations. First, given the location of the ground station in the user hotspot (user cluster) and the spatial distribution of users, we compute the optimal inclination angle and length of the tether. Using these results, we compute the densities of the tethered UAVs deployed at different altitudes, which enables the tractable analysis of the interference in the considered setup. Next, using tools from stochastic geometry and an approach of dividing user clusters into finite frames, we analyze the coverage probability as a function of the maximum tether length, the density of accessible rooftops for UAV ground station deployment, and the density of clusters. We verify our findings using Monte Carlo simulations and draw multiple useful insights. For instance, we show that it is actually better to deploy UAVs at a fraction of the clusters, not all of them as it is usually assumed in the literature.