In the mission of approaching to a disabled tumbling target, the space will be divided into the safe zone and the unsafe zone because of the nutation of the target. During the chaser's flight in the safe zone of the target, the collision possibility between the target and the chaser should be determined to avoid the collision accident. To solve this problem, the region judgment method is used to transform the task into the position relation determination problem between the safe zone of the target and the trajectory of the chaser. By analyzing characteristics of the safe zone of the target as well as the trajectory of the chaser, both the conical safe corridor model of the target and ellipsoidal position error model of the chaser are established. As a result, the problem is further transformed into the issve of position relation determination between the cone and the ellipsoid. Through projective transformation and plane projection, the original cone and ellipsoid are transformed into a circle and an ellipse on the plane with the unchangeable position relation. Using the location criterion of plane curves, the position relation between the circle and ellipse would be determined, and then, the position relation between the cone and ellipsoid could be deduced, which is expected to determine whether the collision risk exists or not. Simulation experiment shows that this method is accurate to determine the position relation between the conical surface and the ellipsoidal surface, and it can be used to detect the collision possibility in the flight during the safe corridor of the target.