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We present a scaled particle density functional study of two-dimensional binary mixtures of hard convex particles with one or both species being ellipses. In particular, we divide our study into two parts. The first part is devoted to the calculation of phase diagrams of mixtures with the same elliptical shapes, but with (i) different aspect ratios and equal particle areas, (ii) equal aspect ratios and different particle areas and (iii) with the former and the latter being different. In the second study we obtain the phase diagrams corresponding to crossed-mixtures of particles with species having elliptical and rectangular shapes. We compare the phase diagram topologies and explain their main features from the entropic nature of particle interactions directly related to the anisotropies, areas and shapes of species. The results obtained can be corroborated by experiments on granular rods where the entropic forces are very important in the stabilisation of liquid-crystal textures at the stationary states.