Answer
Please see the graph.
Work Step by Step
The red graph is $ \frac{x^{2}}{4}+\frac{y^{2}}{9}\ge 1$, and the blue graph is $x^{2}+y^{2}\ge4$.
Both graphs have greater than or equal to signs, so they will have solid lines. We also pick the point $(0,2)$ to determine what sides of the graphs to shade.
$(0,2)$
$\frac{x^{2}}{4}+\frac{y^{2}}{9}\ge1$
$\frac{0^{2}}{4}+\frac{2^{2}}{9}\ge1$
$0/4 + 4/9 \ge 1$
$4/9 \ge 1$ (false, so we shade the side of the graph without the point)
$(0,2)$
$x^{2}+y^{2}\ge4$
$0^{2}+2^{2}\ge4$
$0+4 \ge 4$
$4 \ge 4$ (true, so we shade the side of the graph with the point)
The overlap of the two graphs is the solution set.
