In this study, we investigate structures and stabilities of the micelles of a cyclic amphiphile (c-PBA-b-PEO) composed of poly(n-butyl acrylate) (PBA) and poly(ethylene oxide) (PEO) blocks and its linear diblock and triblock analogues (l-PBA-b-PEO and l-PBA-b-PEO-b-PBA) by using synchrotron X-ray scattering and quantitative data analysis. The comprehensive scattering analysis gives details and insights to the micellar architecture through structural parameters. Furthermore, this analysis provides direct clues for structural stabilities in micelles, which can be used as a good guideline to design highly stable micelles. Interestingly, in water, all topological polymers are found to form ellipsoidal micelles rather than spherical micelles; more interestingly, the cyclic polymer and its linear triblock analog make oblate-ellipsoidal micelles while the linear diblock analog makes a prolate-ellipsoidal micelle. The analysis results collectively inform that the cyclic topology enables more compact micelle formation as well as provides a positive impact on the micellar structural integrity.