  We propose a simulation model to study the properties of directed percolation
in two-dimensional (2D) anisotropic random media. The degree of anisotropy in
the model is given by the ratio $\mu$ between the axes of a semi-ellipse
enclosing the bonds that promote percolation in one direction. At percolation,
this simple model shows that the average number of bonds per site in 2D is an
invariant equal to 2.8 independently of $\mu$. This result suggests that
Sinai's theorem proposed originally for isotropic percolation is also valid for
anisotropic directed percolation problems. The new invariant also yields a
constant fractal dimension $D_{f} \sim 1.71$ for all $\mu$, which is the same
value found in isotropic directed percolation (i.e., $\mu = 1$).
