Answer
$\frac{x^2}{4} + \frac{y^2}{8}=1$
Work Step by Step
Step 1. Identify the given values: use the diagram given in the Exercise, we can identify the minor axis length as $b=2$, and one focal point as $(0,2)$ so that $c=2$.
Step 2. Write a general equation: as the focus is 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 $b=2, c=2$, use the relationship $a^2=b^2+c^2$. we have $a=\sqrt {2^2+2^2}=2\sqrt 2$
Step 4. Conclusion: the equation for the graph can be written as $\frac{x^2}{4} + \frac{y^2}{8}=1$
