If y = mx + 4 is a tangent to both the parabolas y2=4x and  x2=2by, then b is equal to

The given line equation is y = mx+4                       ….(i) The equation of the tangent to the parabola y2=4x is   y=mx+1m                        ….(ii)from (i) and (ii) 4=1m⇒m=14So line y=14x+4 is also tangent to parabola x2=2by , so solvex2=2bx+164, it must have only one solution, it implies that discriminant must be zero. ⇒2x2−bx−16b=0  ⇒D=0⇒b2−4×2×−16b=0     ⇒b2+32×4b=0    b=−128,b=0(not possible)