Answer
$\frac{x^2}{16}+\frac{y^2}{7}=1$
See graph.
Work Step by Step
1. Based on the given conditions, the ellipse has a horizontal major axis with center $(0,0)$ (midpoint between the two foci), thus we have a general form $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
2. With $c=3, a=4$, we have $b^2=a^2-c^2=7$, thus the equation $\frac{x^2}{16}+\frac{y^2}{7}=1$
3. See graph.