Answer
$0.97979$
Work Step by Step
The standard form of an ellipse can be written as: $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1....(1); $and has foci $( \pm c, 0)$ where ; $c^2=a^2-b^2$.
We will divide the given equation of the ellipse by $25$ to obtain:
$\dfrac{x^2}{25}+\dfrac{y^2}{1}=1$
On comparison, we have $a=5$ and $b=1$.
Now, $c^2=a^2-b^2 \implies c^2 =(5)^2-(1)^2 \implies c^2= 24$
or, $c=\sqrt {24}$
The eccentricity of the ellipse can be found as: $e=\dfrac{c}{a}$
Therefore, $e=\dfrac{\sqrt {24}}{5} \approx 0.97979$
