Answer
$\frac{x^2}{36}+\frac{y^2}{16}=1$
Work Step by Step
Foci on x-axis: major axis is horizontal.
Major axis: $length=2a$
$2a=12$
$a=6$
$e=\frac{c}{a}$
$\frac{\sqrt 5}{3}=\frac{c}{6}$
$c=\frac{6\sqrt 5}{3}=2\sqrt 5$
$a^2=b^2+c^2$
$b^2=a^2-c^2=6^2-(2\sqrt 5)^2=36-20=16$
$b=4$
Equation of the ellipse:
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
$\frac{x^2}{6^2}+\frac{y^2}{4^2}=1$
$\frac{x^2}{36}+\frac{y^2}{16}=1$
