Answer
$\displaystyle \frac{(x-5)^{2}}{9}+\frac{(y-2)^{2}}{1}=1$
Work Step by Step
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 $2b$
$2a=8-2=6 \Rightarrow a=3$
$2b=3-1=2\Rightarrow b=1$
$\displaystyle \frac{(x-5)^{2}}{9}+\frac{(y-2)^{2}}{1}=1$
