Answer
Please see the graph.
Work Step by Step
$\sqrt {25} =±5$
$\sqrt 4 = ±2$
We know the boundaries of the ellipse are $(-5,0), (0, -2), (0,2)$, and $(5,0)$. Since we have a $\le$ sign, we use a solid line.
We can pick a point to determine whether to shade inside or outside the ellipse. We pick $(0,0)$.
$\frac{x^2}{25} + \frac {y^2}{4} \le 1$
$\frac{x^2}{25} + \frac {y^2}{4} \le 1$
$\frac{0^2}{25} + \frac {0^2}{4} \le 1$
$\frac{0}{25} + \frac {0}{4} \le 1$
$0 + 0 \le 1$
$0 \le 1$ (true)
This is true, so we shade inside the ellipse.
