Answer
$e=\dfrac{2\sqrt{6}}{5} \approx 0.98$
Work Step by Step
Divide the given equation of the ellipse by $25$.
$\dfrac{x^2}{25}+\dfrac{y^2}{1}=1$
The ellipse above has $a^2=25$ so $a=5$, and $b^2=1$ which means $b=1$.
Solve for $c$ using the formula $c^2=a^2-b^2$ to obtain:
\begin{align*}
c^2&=25-1\\
c^2&=24\\
c&=\sqrt {24}\\
c&=2\sqrt6
\end{align*}
Thus,
$$e=\dfrac{2\sqrt{6}}{5} \approx 0.98$$
