#### Answer

See the explanation below.

#### Work Step by Step

Standard equation for ellipse is $\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}$
Here, $(h,k)$ represents center.
On comparing the $\dfrac{(x+1)^2}{25}+\dfrac{(y-4)^2}{9}$ with the standard form, we have center at $(-1,4)$.