Let y=p(x) be the parabola passing through the points (-1,0),(0,1) and (1,0). If the area of the region {(x, y):(x+1)^2+(y-1)^2 ≤ 1, y ≤ p(x)} is A,…

Let $\displaystyle y=p(x)$ be the parabola passing through the points $\displaystyle (-1,0),(0,1)$ and $\displaystyle (1,0)$. If the area of the region $\displaystyle \left\{(x, y):(x+1)^2+(y-1)^2 \leq 1, y \leq p(x)\right\}$ is A , then $\displaystyle 12(\pi-4 A)$ is equal to $\displaystyle \_\_\_\_$.