Answer
Please see the graph.
Work Step by Step
$x^2+y^2 >4$
This is the equation of a circle with radius 2. If a point is a valid solution to the inequality, then it will be inside the circle. We pick the point $(4,1)$ to determine if this is part of the solution set.
$x^2+y^2>4$
$4^2+ 1^2 > 4$
$16 +1 >4$
$17 > 4$ (true)
This point is outside the circle, so it is part of the shaded region.
