# 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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