We focus on recovering the 2D Euclidean structure in one view from the projections of N parallel conics in this paper. This work denotes that the conic dual to the absolute points is the general form of the conic dual to the circular points, but it does not encode the Euclidean structure. Therefore, we have to recover the circular point-envelope to find out some useful information about the Euclidean structure, which relies on the fact that the line at infinity and the symmetric axis can be recovered. We provide a solution to recover the two lines and deduce the constraints for recovering the conic dual to the circular points, then apply them on the camera calibration. Our work relaxes the problem conditions and gives a more general framework than the past. Experiments with simulated and real data are carried out to show the validity of the proposed algorithm. Especially, our method is applied in the endoscope operation to calibrate the camera for tracking the surgical tools, that is the main interest-point we pay attention to.