Moving points and constant area

Calculus Level 3

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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