In this paper, the off-design condition of a supersonic intake where the lip generated expansion fan interacts with the incident shock and the Mach stem (called Type 2 Mach reflection) is investigated. Because of the presence of the expansion fan, the incident shock becomes curved and the curvature of the Mach stem changes in a significant fashion. The flow in the region downstream of the incident and reflected shocks is also affected by the presence of the expansion waves transmitted from the incident shock. An analytical solution based on the procedures of Gao and Wu (2010) and Bai and Wu (2017) taking into account all these effects has been obtained which gives the shapes of the incident shock, reflected shock, slipline and the Mach stem. The results are compared with the numerical solution obtained using a higher order Runge-Kutta discontinuous Galerkin method.