  We show within the slave-boson mean field approximation that the
two-dimensional t-J model has an intrinsic instability toward forming a
quasi-one-dimensional (q-1d) Fermi surface. This q-1d state competes with, and
is overcome by, the d-wave pairing state for a realistic parameter choice.
However, we find that a small spatial anisotropy in t and J exposes the q-1d
instability which has been hidden behind the d-wave pairing state, and brings
about the coexistence with the d-wave pairing. We argue that this coexistence
can be realized in La_{2-x}Sr_{x}CuO_4 systems
