This paper addresses the problem of camera calibration and shape recovery using a single image of a reflectively symmetric object. Unlike existing methods requiring knowledge of 3D points or two images, this paper proposes to calibrate camera parameters using one image with known point distance ratios on 3D object. Specifically, we first recover the vanishing point of the symmetry plane normal. Then a set of candidate focal lengths are uniformly selected as the initial values, from which the pan and yaw angles of the camera can be obtained. To recover 3D points on the object, we recover the ratio of depth scale factors between symmetric 2D point pairs, then the ratio of depth scale factors between different symmetric points. Finally, constraints from 3D distance ratios on the object are used to refine the estimation of camera parameters. Both synthetic and real experiments demonstrate the feasibility of our method.