  We study the effects of anisotropic interactions in the quantum Hall effect
in the presence of a fourfold discrete rotational ($C_4$) symmetry. Employing
the density matrix renormalization group technique on an infinite cylinder
geometry (iDMRG), we calculate the anisotropy response of the Laughlin state at
$\nu=1/3$ and the composite-Fermi liquid (CFL) state at $\nu=1/2$. We find that
the anisotropy transferred from the interaction potential to the $\nu=1/3$
state is stronger when compared to the complementary case of an anisotropic
band. Further, the strength of anisotropy reduces as the interaction is made
shorter ranged. Quite surprisingly, at $\nu=1/2$, we find that the deformation
in the CF Fermi-surface changes sign as the interaction range is reduced. Our
results imply that the short-distance and long-distance parts of the
interaction potential have opposite effects on the CFL state in the presence of
$C_4$-symmetric anisotropy.
