The directional dependence of the correlation length of the hard-hexagon model is calculated by a new method which introduces the shift operator into the usual transfer matrix method. This method is also applied to the calculation of the interfacial tension of the hard-hexagon model, which is anisotropic. In addition, the equilibrium droplet shape of one phase embedded inside another is obtained from the analysis of the interracial tension by the use of Wulff's construction.