Step 1:
$25x^2-16y^2=400$
The above equation is divided by $400$ we get
$\large\frac{x^2}{16}-\large\frac{y^2}{25}$$=1$
$a^2=16,b^2=25$
$\Rightarrow a=4,b=5$ and the axis is the transverse axis.
Step 2:
Ecentricity $e=\sqrt{1+\large\frac{b^2}{a^2}}=\sqrt{1+\large\frac{25}{16}}=\large\frac{\sqrt{41}}{4}$
Step 3:
Centre : Origin $O(0,0)$
Step 4:
Foci : $(\pm ae,0)$
$ae=4\times \large\frac{\sqrt{41}}{4}$
Foci $(\pm \sqrt{41},0)$
Step 5:
Vertices : $(\pm a,0)$
$\Rightarrow (\pm 4,0)$