Correct option is (d) y=x+2
Explaination::
tangents to the curve y^{2}=8x is y=mx+2/m , so it must satisfy xy=-1
\(x({mx+\frac{2}{m}})=-1\)
\(mx^2+\frac{2}{m}x+1=0 ,\)
since it has equal roots , therefore D=0
\(\frac{4}{m^2}-4m=0\)
\(m^3=1 \)
m=1
therefore , the equation of commom tangent is y=x+2