Mathematics

Problem

A point

P

lying inside the curve

y = \sqrt{2ax - x^2}

is moving such that its shortest distance from the curve at any position is greater than its distance from

X

-axis. The point

P

encloses a region whose area is equal to a.

\frac{\pi a^2}{2}

\frac{a^2}{3}

\frac{2a^2}{3}

\left( \frac{3\pi - 4}{6} \right) a^2