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