Broken symmetry adds to the tunability of nanoparticles, which increases the flexibility of the design process, but, on the other hand, complicates the modeling process, due to the additional parameters and the symmetry breaking. In this paper, we present an analytical analysis scheme for the properties of non-concentric core-shell particle sensors based on the quasistatic approximation. We use our scheme to study the sensitivity of the nanoparticle, its Q-factor, and the stability of the Q-factor for changing outer dielectric constant.