2D arc well trajectory is considered with priority in conventional deviated and horizontal well design. However, because there are a lot of combination forms of hole sections and also a lot of resolution combinations of unknowns for the same hole section, the computation is very complicated to derive the computation formula for the solutions of each hole section combination and each solving combination. This paper studies the general solutions of arbitrary hole section combination and arbitrary solving combination, discovers that the constraint equation of hole trajectory design can be dissolved into linear algebra equation system or one of the four typical systems of equations. The computation formula of the real number solutions of the four typical equation systems is obtained and the discretion conditions of real number solution are given. This study has important significance for fundamental research and computer software development for 2D arc borehole trajectory design.