## College Algebra (6th Edition)

$\displaystyle \frac{x^{2}}{4}+\frac{y^{2}}{8}=1$
With the given information, the foci are $c=2$ units above/below the point (0,0) the major axis is vertical, so the standard form the equation is $\displaystyle \frac{(x-h)^{2}}{b^{2}}+ \displaystyle \frac{(y-k)^{2}}{a^{2}}=1$ The x-intercepts give: $b=2$. $(h,k)=(0,0)$ $b=2$ $c=2$ From $c^{2}=a^{2}-b^{2}$ $a^{2}=b^{2}+c^{2}=4+4=8$ so the equation is $\displaystyle \frac{x^{2}}{4}+\frac{y^{2}}{8}=1$