This paper studies a vertical powered descent problem in the context of planetary landing, considering glide-slope and thrust pointing constraints and minimizing any final cost. After stating the Max-Min-Max or Max-Singular-Max form of the optimal control deduced from the Pontryagin Maximum Principle, it theoretically analyzes the optimal trajectory for a more specific problem formulation to show that there can be at most one contact or boundary interval with the state constraint on each Max or Min arc.