Official solution
Given y = mx + 4 is tangent to both the parabolas.
\[ \therefore \] Applying condition of tangent
for y2
= 4x, we get
\[{1 \over m}\] = 4
\[ \Rightarrow \] m = \[{1 \over 4}\]
For x2
= 2by line y = \[{x \over 4}\] + 4 is tangent
\[ \therefore \] x2 = 2b\[\left( {{x \over 4} + 4} \right)\]
\[ \Rightarrow \] x2 - \[{{bx} \over 2}\] - 8b = 0
For tangent to the parabola Discriminant = 0
\[ \Rightarrow \] \[{{{b^2}} \over 4}\] + 32b = 0
\[ \Rightarrow \] b = -128