  An impurity atom immersed in an ultracold atomic Fermi gas can form a
quasiparticle, so-called Fermi polaron, due to impurity-fermion interaction. We
consider a three-dimensional homogeneous dipolar Fermi gas as a medium, where
the interatomic dipole-dipole interaction (DDI) makes the Fermi surface
deformed into a spheroidal shape, and, using a Chevy-type variational method,
investigate the ground-state properties of the Fermi polaron: the effective
mass, the momentum distribution of a particle-hole (p-h) excitation, the drag
parameter, and the medium density modification around the impurity. These
quantities are shown to exhibit spatial anisotropies in such a way as to
reflect the momentum anisotropy of the background dipolar Fermi gas. We have
also given numerical results for the polaron properties at the unitarity limit
of the impurity-fermion interaction in the case in which the impurity and
fermion masses are equal. It has been found that the transverse effective mass
and the transverse momentum drag parameter of the polaron both tend to decrease
by $ \sim 10\%$ when the DDI strength is raised from $0$ up to around its
critical value, while the longitudinal ones exhibit a very weak dependence on
the DDI.
