HMMT 2015 G8

Geometry
Answer

Let $S$ be the set of discs $D$ contained completely in the set $\{(x, y): y<0\}$ (the region below the $x$ -axis) and centered (at some point) on the curve $y=x^{2}-\frac{3}{4}$ . What is the area of the union of the elements of $S$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{2 \pi}{3}+\frac{\sqrt{3}}{4}

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