MathNet 2015-part-07 — 185 problems (EN–VI) Question 53

Let $S$ be the set of discs $D$ contained completely in the set $\{(x, y): y\lt 0\}$ (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 $S$?