Perpendicular is drawn from a fixed point  $(3,4)$ to a variable line which cuts positive x-axis at one unit distance from origin. Circle  $S(x,y)=0$  represents the locus of the foot of perpendicular drawn from point  $(3,4)$ to the variable line. If radius of  $S(x,y)=0$ is  $\sqrt{{\lambda }_1}$ and length of tangent drawn to  $S(x,y)=0$ from origin is  $\sqrt{{\lambda }_2},$ then find the value of  ${\lambda }_1+{\lambda }_2.$