The points of intersection of the line a x+b y=0,(a ≠ b) and the circle x^2+y^2-2 x=0 are A (α, 0) and B (1, β). The image of the circle with AB as a…

The points of intersection of the line $\displaystyle a x+b y=0,(a \neq b)$ and the circle $\displaystyle x^2+y^2-2 x=0$ are $\displaystyle \mathrm{A}(\alpha, 0)$ and $\displaystyle \mathrm{B}(1, \beta)$. The image of the circle with AB as a diameter in the line $\displaystyle x+y+2=0$ is :