This paper presents the method to obtain, in Cartesian coordinates, the parallel curve lines of non-degenerate conical curves, by analytical and numerical methods. Offset is defined as parallel function to the original function to a distance r. Offset of a conic is important for the manufacturing processes of mechanisms, lenses, mirrors, and molds; especially in the turning with computerized numerical control (CNC) of surfaces of revolution with conical sections, using diamond tools of radio r. Also a refined tip technique using segmental circular interpolation to numerically construct the parabola offset is presented, that also can be used as model to determine offsets of ellipse and hyperbola.