Catadioptric systems are realizations of omnidirectional vision through mirror-lens combinations. Designs preserving the uniqueness of an effective viewpoint have recently gained attraction. We present here a novel approach for estimating the intrinsic parameters of a well-known catadioptric system consisting of a paraboloid mirror and an orthographic lens. We introduce the geometry of catadioptric line projection and we show that the vanishing points lie on a conic section which encodes the entire calibration information. Projections of two sets of parallel lines suffice for intrinsic calibration from one view as well as for metric rectification of a plane. Our approach overcomes limitations of existing manual calibration methods and was successfully tested on the task of back-warping real-images images onto virtual planes.