Answer
$\frac{x^2}{16} + \frac{y^2}{25}=1$
Work Step by Step
Step 1. Identify the given values: Foci $(0, \pm3), c=3$, vertices: $(0, \pm5), a=5$
Step 2. Write a general equation: since the vertices are on the y-axis, we can write an equation as $\frac{x^2}{b^2} + \frac{y^2}{a^2}=1$ where $a\gt b\gt0$.
Step 3. Find the unknowns: with $a=5, c=3$, we have $b^2=a^2-c^2=16$ and $b=4$.
Step 4. Conclusion: the equation can be written as $\frac{x^2}{16} + \frac{y^2}{25}=1$
