Straight Lines And Pair Of Straight Lines

$(0, k)$ is the point to which the origin is to be shifted by the translation of the axes so as to remove the first degree terms from the equation $a x^2-2 x y+b y^2-2 x+4 y+1=0$ and $\frac{1}{2} \tan ^{-1}(2)$ is the angle through which the coordinate axes are to be rotated about the origin to remove the $x y$-term from the given equation, then $a+b=$