Solution :
Any tangent to the parabola y^ 2 = 4x is y =mx + a/m
comparing it with y = mx + 4 ,we get m =1/4
Equation of tangent becomes y = x/4 + 4
y = x/4 + 4 is a tangent to x^2 = 2by
Now
x^2 = 2b ( x/4 +4)
or 2x^2 - bx -16b =0
D = 0
b^2 + 128 b = 0
b = - 128 ANS