  We show that the small scatter around the Fundamental Plane (FP) of massive
elliptical galaxies can be used to derive important properties of their dark
and luminous matter. The central velocity dispersion sigma_0, appearing in
(e.g.) the Fundamental Plane, is linked to photometric, dynamical and
geometrical properties of (luminous and dark) matter. We find that, inside the
effective radius R_e, the matter traced by the light must largely dominate over
the dark matter (DM), in order to keep the ellipticals close enough to the FP.
This recalls analogous findings for spiral galaxies.
  In particular we also find that cuspy DM distributions, as predicted by
numerical simulations in Lambda CDM cosmology, are unable to explain the very
existence of the FP; in fact, according to this theory, the structural
properties of dark and luminous matter are so interwoven that a curved surface
is predicted in the log-space (sigma_0, R_e, L), rather than a plane. In order
to agree with the FP, CDM halos must have concentrations parameters in the
range of 5-9 (i.e. values significantly lower than the current predictions).
  Assuming a more heuristic approach and allowing for cored DM halos, we find
that the small intrinsic scatter of the FP yields to i) an average value for
the dark-to-light-traced mass ratio inside the length-scale of light R_e of
about 0.3, ii) a mass-to-light ratio of the matter traced by the light
increasing with spheroid luminosity as L^(0.2) in Gunn-r band, with a value of
5.3 at L = 2.7 x 10^{10} L_{sol}.
