## Calculus (3rd Edition)

$$\left(\frac{x}{5}\right)^{2}+\left(\frac{y}{7}\right)^{2}=1.$$
Since the vertices are at $(\pm 5,0)$ and $(0,\pm7)$, then we have $$a=5, \quad b=7$$ and hence the ellipse is centered at the origin and has the equation $$\left(\frac{x}{5}\right)^{2}+\left(\frac{y}{7}\right)^{2}=1.$$