Answer
Please see the graph.
Work Step by Step
$\frac{x^{2}}{25}+\ \frac{y^{2}}{4}\le1$
This formula is for an ellipse, and this divides the plane into two regions--the inside and the outside. We pick the point $(0,0)$ to see what region this point is in.
$\frac{x^{2}}{25}+\frac{y^{2}}{4}\le1$
$\frac{0^{2}}{25}+\frac{0^{2}}{4}\le1$
$\frac{0}{25}+\frac{0}{4}\le1$
$0+0 \le 1$
$0 \le 1$ (true)
We shade the inside of the ellipse.
