Let (d y)/(d x)=(a x- b y+ a)/(b x+ c y+ a), a, b, c ∈ R, represents a circle with center (α, β). Then, α+2 β is equal to:

Let $\displaystyle \frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\mathrm{a} x-\mathrm{b} y+\mathrm{a}}{\mathrm{b} x+\mathrm{c} y+\mathrm{a}}, \mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbf{R}$, represents a circle with center $\displaystyle (\alpha, \beta)$. Then, $\displaystyle \alpha+2 \beta$ is equal to :