## College Algebra (6th Edition)

$\displaystyle \frac{(x-5)^{2}}{9}+\frac{(y-2)^{2}}{1}=1$
Endpoints of major axis have the same y-coordinate,so the major axis is horizontal, so $\displaystyle \frac{(x-h)^{2}}{a^{2}}+ \displaystyle \frac{(y-k)^{2}}{b^{2}}=1$ is the equation form. The center is the midpoint of the vertices: $(h,k)=(\displaystyle \frac{2+8}{2},\frac{2+2}{2})=(5,2)$ Major and minor axes have lengths $2a$ and $2b$ $2a=8-2=6 \Rightarrow a=3$ $2b=3-1=2\Rightarrow b=1$ $\displaystyle \frac{(x-5)^{2}}{9}+\frac{(y-2)^{2}}{1}=1$