If a tangent drawn at the point \(P(h,k)\), where \(h,k\in \mathbb{Z}\), on the curve
\[
y=2x^3+3x^2-4x-1
\]
passes through the point \(Q(2,8)\), then \(PQ=\)
Show Hint
When a tangent passes through a fixed external point, write the tangent equation at a general point \((h,f(h))\) and substitute the external point into it. This converts the problem into an algebraic equation in \(h\).