Under the constrains of single-viewpoint and the requirements of the specific detector and vertical field of view, the equations of eccentricity, thickness of the hyperbolic mirror, install distance and the geometric constraints of single viewpoint hyperbolic catadioptric infrared panoramic imaging system which utilizes the quadratic surface of reflective mirror were derived. At the same time, as for the hyperbolic mirror, the equation of the resolution which include instantaneous field of view in the vertical direction and instantaneous field of view in the horizontal direction of the single viewpoint hyperbolic catadioptric infrared panoramic imaging system were deduced. Under the situation of ideal atmosphere, high target contrast, the simplest range equation which combined with the NVThermIP model was established. The simulation was under the conditions of different size and sensitivity of the detector. The simulation results show that: the spatial resolution of the system increases with the increase of the size of the detector; the range performance of the system increases with the increase of the size and sensitivity of the detector. However the increase of sensitivity is not obvious to the improvement of the range performance.