Mathematics Question from JEE Main 2024 · 30 January, Shift 2

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 coordinate axes, where $(x, y)$ is any point on the curve, is always $A = -\frac{y^2}{2Y'(x)} + 1$. If $Y(1) = 1$, then $12Y(2)$ equals: