Abstract: The Five-hundred-meter Aperture Spherical radio Telescope (FAST) can change the shape of its illuminated area of the spherical reflector into a paraboloid of 300 m aperture, which realized the primary reflector antenna function of the telescope. The illuminated aperture of the telescope (the aperture of the paraboloid that changed from the spherical reflector) plays a key role in the performance of the telescope. In order to improve the potential performance and for the subsequent development of the telescope, as the illuminated aperture of FAST is 300 m and larger than 300 m, by calculating the shape-changing between paraboloid with different focal lengths and the reference spherical reflector, the analysis of the shape-changing from the spherical reflector to the paraboloid is carried out, and the feasibility of other illuminated aperture for the telescope is discussed. The focal length and the focal ratio of the paraboloid in the maximum movement distance of the actuator are given. In terms of the driving distance, the theoretical feasibility of the shape-changing is explored. The analysis is also applicable to the paraboloid of other apertures.