  We report the $^{59}$Co NMR studies of the in-plane anisotropy of bilayer
hydrated Na$_{x}\mathrm{CoO_{2}} \cdot$$y\mathrm{H_{2}O}$ using a oriented
powder sample by a magnetic field in Fluorinert FC70. We found for the first
time the $ab$-plane anisotropy of the $^{59}$Co NMR Knight shift $K$, the
nuclear spin-lattice relaxation rate 1/$T_{1}$ and the nuclear spin-spin
relaxation rate 1/$T_{2}$ at a magnetic field $H \sim$ 7.5 T up to 200K. Below
75 K, the anisotropy of $K$ is large compared with that at high temperatures.
The hyperfine coupling constants seem to change around the temperature 150 K,
in which the bulk susceptibility $\chi$ shows broad minimum, suggesting a
change of the electronic state of CoO$_{2}$ plane. 1/$T_{1}$ also shows a
significant anisotropy, which cannot be explained only by the anisotropy of the
hyperfine coupling constants nor the anisotropic uniform spin susceptibility.
The difference in the in-plane anisotropy of $T_{1}$ from that of $K$ indicates
that the magnetic fluctuation at a finite wave vector $\vec{q} \neq 0$ is also
anisotropic and the anisotropy is different from that at $\vec{q} = 0$.
