Explanation
\begin{aligned}
& \mathrm{We~have,~T=S_{1}} \\
& \Rightarrow{\frac{x}{25}}+{\frac{y\times{\frac{2}{5}}}{16}}={\frac{1}{25}}+{\frac{4}{16\times25}} \\
& \Rightarrow\frac{x}{25}+\frac{y}{40}=\frac{1}{25}+\frac{1}{100}=\frac{4+1}{100} \\
& \Rightarrow\frac{x}{25}+\frac{y}{40}=\frac{1}{20}\Rightarrow\frac{8x+5y}{200}=\frac{1}{20} \\
& \Rightarrow8x+5y-10=0 \\
& :{\frac{x^{2}}{25}}+{\frac{y^{2}}{16}}=1 \\
& \Rightarrow\frac{16x^{2}+25y^{2}}{400}=1\Rightarrow16x^{2}+25y^{2}=400 \\
& \text{一}>16x^{2}+100+64x^{2}-160x=400
\end{aligned}
⇒80x2−160x−300=0
⇒2x2−40x−75=0
⇒4x2−8x−15=0
Now, chord length =(x2−x1)2+(y2−y1)2
=(x2−x1)2+2564(x2−x1)2=2589(x2−x1)2
=589(x2−x1)
∴ Required distance =589⋅19=51691
