Answer
$\frac{x^2}{7}+\frac{y^2}{16}=1$
See graph.
Work Step by Step
1. Known an ellipse with center $(0,0)$, vertex $(0,-4)$ and focus $(0,3)$, we can find it has a vertical major axis with a general form $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
2. With $a=4, c=3$ and $b^2=a^2-c^2=7$, we have $\frac{x^2}{7}+\frac{y^2}{16}=1$
3. See graph.
