Application Of Derivatives

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