In this article, we study the formation problem for a group of mobile agents in a plane, in which the agents are required to maintain a distribution pattern, as well as to rotate around or remain static relative to a static/moving target. The prescribed distribution pattern is a class of general formations where the distances between neighboring agents or the distances between each agent and the target do not need to be equal. Each agent is modeled as a double integrator and can merely perceive the relative information of the target and its neighbors, and the acceleration of the target. In order to solve the formation problem, a limit-cycle-based controller design is delivered. We divide the overall control objective into two subobjectives, where the first is target circling that each agent keeps its own desired distance to the static/moving target as well as rotating around or remaining static relative to the target as expected, and the second is distribution adjustment that each agent maintains the desired distance to its neighbors. Then, we propose a controller comprised of two parts, where a limit cycle oscillator named a converging part is designed to deal with the first subobjective, while a layout part is introduced to address the second subobjective. One key merit of the controller is that it can be implemented by each agent in its local frame so that only local information is utilized without knowing global information. Theoretical analysis of the convergence to the desired formation, of which the agents are required to be evenly distributed on a circle around the target, is provided for the multiagent system under the proposed controller. Numerical simulations are given to validate the effectiveness of the proposed controller for the cases of general formations, and to show that no collision between agents ever takes place throughout the system's evolution.