Answer
See graph and explanations.
Work Step by Step
Step 1. Given $\frac{x^2}{81/4}+\frac{y^2}{25/16}=1$, we can identify $a^2=\frac{81}{4}, b^2=\frac{25}{16}$; thus $c=\sqrt {a^2-b^2}=\frac{\sqrt {299}}{4}$. The ellipse is centered at $(0,0)$ with a horizontal major axis.
Step 2. We can graph the equation as shown in the figure, and the foci can be located at $(\pm\frac{\sqrt {299}}{4},0)$