Based on the equations of missile motion with respect to the desired terminal line of sight (DTLOS), the extended proportional navigation and extended optimal guidance law with impact angle constraint was deduced for lag-free system when -n power of time-to-go was introduced into the object function. The concept of the generalized optimal guidance law (GOPL) was proposed and the expressions and meaning of which in two different frames of reference were demonstrated. For the GOPL in the DTLOS frame, the analytical solutions of the closed-form trajectory were derived according to the method of power series and the analytical position, velocity and acceleration command were obtained. Finally, the analytical solutions were validated by the simulation results.