Let Y=Y(X) be a curve lying in the first quadrant such that the area enclosed by the line Y-y=Y^′(x)(X-x) and the co-ordinate axes, where (x, y) is…

Let $\displaystyle Y=Y(X)$ be a curve lying in the first quadrant such that the area enclosed by the line $\displaystyle Y-y=Y^{\prime}(x)(X-x)$ and the co-ordinate axes, where $\displaystyle (x, y)$ is any point on the curve, is always $\displaystyle \frac{-y^2}{2 Y^{\prime}(x)}+1, Y^{\prime}(x) \neq 0$. If $\displaystyle Y(1)=1$, then $\displaystyle 12 Y(2)$ equals $\displaystyle \_\_\_\_$.