Let a curve y=f(x), x in (0,oo) pass thr...

Let a curve `y=f(x), x in (0,oo)` 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-axis at the point `S(0,c)` such that `bc=3`, then `(PQ)^2` is equal to ______

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