Geostationary Orbit (GEO) spacecraft are critical space assets and pivotal in space situational awareness. This paper addresses China's space security requirements by conducting coverage analysis of high-orbit space targets from a space-based observation platform. Initially, a novel load element model for space-based observation platforms is introduced, alongside an equation for GEO target observation. Solving this equation delineates the field of view mapping domain on a two-dimensional plane, with the trajectory of the platform represented as a line segment. This reformulates the observation window issue for GEO targets into a trajectory intersection problem on the plane. To address the issue of quasi GEO target coverage analysis, we propose the concept of equivalent Earth rotation angular velocity and improve the field of view mapping domain method for solution. Additionally, the concept of a multi-star relative field of view mapping domain is introduced, extending the single-star coverage analysis to constellation coverage scenarios. Extensive simulation experiments reveal that the visible window calculation error of the proposed method is smaller than 0.1 s when compared to STK calculations, thereby validating effectiveness of the proposed model and method.