Answer
$\dfrac{x^2}{1600}+\dfrac{y^2}{1536}=1$
Work Step by Step
The eccentricity of the ellipse $\dfrac{x^2}{m^2}+\dfrac{y^2}{n^2}=1$ when $m \gt n$ is given by:
$e=\dfrac{\sqrt {m^2-n^2}}{m}$
The foci of the ellipse are: $(\pm me,0)$ and the directrices are given as: $x=\pm \dfrac{m}{e}$
Given: $e=0.2$ ; foci: $(\pm 8,0)$
Now, $m=\dfrac{c}{e}=\dfrac{8}{0.2}=40$ and $n^2=1600-64=1536$
so, the equation of the ellipse is:
$\dfrac{x^2}{1600}+\dfrac{y^2}{1536}=1$
