If reflection of the parabola  $y^2=4(x-1)$ in the line $x+y=2$ is the curve $Ax+By=x^{2,}$  then the value of (A+B) is

Let a variable point on the parabola be $(1+t^2,2t)$  and its reflection in the givenline be (h,k)

$$\begin{gathered} h-{(1+t)}^2=k-2t=\frac{-2(1+t^2+2t-2)}{2} \\ h-(1+t^2)=1-t^2=-2t+2\Rightarrow h=2(1-t)andk=-(t^2-1) \\ \frac{k}{h}=\frac{-(t-1)(t+1)}{2(1-t)}\therefore t+1=\frac{2k}{h}andt=\frac{2k}{h}-1and1-t=2-\frac{2k}{h}=\frac{h}{2} \\ 2h-2k=\frac{h}{2} 4x-4y=x^2 \\ A+B=0 \end{gathered}$$