The locus given by $25x^2+16y^2=400$is

Given $25x^2+16y^2=400$

$\frac{x^2}{\left(\frac{400}{25}\right)}+\frac{y^2}{\left(\frac{400}{16}\right)}=1$

$\frac{x^2}{16}+\frac{y^2}{9}=1$

Here $a=25,b=16,c=100$

$h=0\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}{h}^2<ab$

And $\Delta =abc\ne 0$

Locus represents a “Ellipse”