Answer
$\frac{x^2}{25} + \frac{y^2}{50}=1$
Work Step by Step
Step 1. Identify the given values: length of minor axis $2b=10$, so that $b=5$, point $(\sqrt 5, \sqrt {40})$ is on the ellipse.
Step 2. Write a general equation: since the foci 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 the equation and $b=5$, plug-in the coordinates of the point, we have
$\frac{5}{5^2} + \frac{40}{a^2}=1$ which gives $a^2=50$
Step 4. Conclusion: the equation can be written as $\frac{x^2}{25} + \frac{y^2}{50}=1$
