We study superdense relativistic stars with anisotropic matter distributions with spheroidal spatial hypersurfaces. We propose a methodology to make an anisotropic generalization of the Vaidya-Tikekar superdense star model. The anisotropic Einstein field equations can be solved in terms of hypergeometric functions for our choice of gravitational potential and anisotropy. Particular parameter choices allow us to generate models of anisotropic stars in terms of elementary functions. Also, isotropic stars can be generated in the limit of vanishing anisotropy. In particular, we obtain the well known superdense models of Tikekar which are isotropic and have specific spheroidal geometries. The impact of anisotropy on the gross physical behaviour of a compact star is studied.