Answer $A$
Let radius of the circle be $r$, then:$$ r = 2\sqrt2$$
Draw perpendiculars from this point to $x$ and $y$ axes respectively and let them be $a$ and $b$.
Now,
$$a^2 + b^2 = r^2 \implies 2a^2 = r^2 \;\because (a = b)$$
$$\implies 2a^2 = (2\sqrt2)^2 = 4 \times 2 \implies a = \pm2$$
So, the coordinates are $(2, -2)$
$\therefore A$ is the correct option.