  The Fermi surface (FS) of an extended $d-p$ Hubbard model is investigated by
a two-pole approximation in both situations with hole and electron doping.
Using the factorization procedure proposed by Beenen and Edwards,
superconductivity with singlet $d_{x^2-y^2}$-wave pairing is considered. The
effects of the $d-p$ hybridization on the FS are the main focus in the present
work. Nevertheless, the asymmetries between the hole- and electron-doped
regimes and the effects of doping and Coulomb interaction on FS are also
investigated. Particularly, it is shown that the crossover from hole-like to
electron-like FS is deeply affected by the $d-p$ hybridization in the
hole-doped case. It has been verified that the effect of the hybridization is
very pronounced around the saddle points $(0,\pm\pi)$ and $(\pm\pi,0)$, where
the intensity of the superconducting order parameter is maximum in the
particular case of $d_{x^2-y^2}$-wave symmetry. In the electron-doped case, the
crossover in the FS is not verified. The doping dependence of the FS topology
in the hole- and electron-doped regimes is in agreement with recent
experimental ARPES results for La$_{2-x}$Sr$_{x}$CuO$_4$ (hole doping) and
Nd$_{2-x}$Ce$_x$CuO$_4$ (electron doping).
