Let a curve y=f(x), x ∈(0, ∞) pass through the points P(1, 3/2) and Q(a, 1/2). If the tangent at any point R(b, f(b)) to the given curve cuts the y…

Let a curve $\displaystyle y=f(x), x \in(0, \infty)$ pass through the points $\displaystyle P\left(1, \frac{3}{2}\right)$ and $\displaystyle Q\left(a, \frac{1}{2}\right)$. If the tangent at any point $\displaystyle R(b, f(b))$ to the given curve cuts the y -axis at the point $\displaystyle S(0, c)$ such that $\displaystyle b c=3$, then $\displaystyle (P Q)^2$ is equal to $\displaystyle \_\_\_\_$.