Answer
The simplified form is, $\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{25}=1$.
Work Step by Step
The provided equation is:
$25{{x}^{2}}+16{{y}^{2}}=400$
Bring it to the standard form of an ellipse, as below:
$\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$
So, divide the equation by $400$ on both sides to get:
$\begin{align}
& \frac{25{{x}^{2}}}{400}+\frac{16{{y}^{2}}}{400}=\frac{400}{400} \\
& \frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{25}=1
\end{align}$
Hence, the required simplified form of the provided equation is $\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{25}=1$.
