Precalculus (6th Edition) Blitzer

$\frac{5x^2}{36}+\frac{y^2}{36}=1$
Step 1. We assume the vertices are along the major axis; thus $a=6$ and the major axis is vertical. Step 2. We can assume the equation as $\frac{x^2}{b^2}+\frac{y^2}{36}=1$ Step 3. As point $(2,-4)$ is on the curve, we have $\frac{2^2}{b^2}+\frac{(-4)^2}{36}=1$, which gives $b^2=\frac{36}{5}$ Step 4. We have the equation as $\frac{5x^2}{36}+\frac{y^2}{36}=1$