Within the frame of a simple, long-wavelength, quasi-static description, we present a theoretical characterization of the optical response of metal nanoparticles doped with active gain elements in a core-shell (metallic core within an active dielectric shell) and nano-shell (active dielectric core within a metallic shell) configurations. The common feature of these structures is that, adding gain to the system produces an increase of the quality of the plasmon resonance, which becomes sharper and sharper until a singular point, after which, the system switches from absorptive to emissive (nanolaser). We use this aforementioned simple model to develop a general method allowing us to calculate both the expected singular plasmon frequency and the gain level needed to realize it and to discuss the spectral deformation occurring before and after this singular point. Finally, we propose a way to calculate if the singular behavior is reachable using realistic amounts of gain.