Two points $P=(a, a^2)$ and $Q=(b, b^2)$$(a < b)$ are moving along the parabola $y=x^2$. If the area of the region bounded by $y=x^2$ and the line segment $PQ$ is always $36$, what is $\displaystyle \lim_{a \to \infty} \frac{\overline{PQ}}{a}$?

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