The Weibull distribution has received a great deal of attention since 1970. In Russian statistical literature, this distribution is often referred to as the Weibull-Gnedenko distribution. It has been applied to model a wide range of data secured from problems such as the yield strength of Boforsí steel, the fiber strength of Indian cotton, the fatigue life of ST-37 steel, the statures of adult males born in the British Isles, and breadth of beans of Phaseolus vulgaris. Many authors used this distribution in their reliability and quality control work. Instead of using the classical approach by solving a pair of differential equations, in this paper, we adopt the well-known Darboux Theory by solving a partial differential equation to find the geodesic equation of two parameter Weibull distributions.