#### Answer

$\dfrac{x^2}{16}+\dfrac{y^2}{4}=1$

#### Work Step by Step

Standard equation for ellipse for horizontal major axis is:$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$
Standard equation for ellipse for vertical major axis is:$\dfrac{(x-h)^2}{b^2}+\dfrac{(y-k)^2}{a^2}=1$
Here, $(h,k)$ represents center with foci $c$ and $c^2=a^2-b^2$
Since, we can be found from the given graph that center is (0,0) for horizontal major axis, we have $a=4, b=2$
This, the equation of ellipse is:
$\dfrac{x^2}{4^2}+\dfrac{y^2}{2^2}=1$
or, $\dfrac{x^2}{16}+\dfrac{y^2}{4}=1$