The length of the chord of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ whose mid-point is $(1,\frac{2}{5})$ , is equal to: 

Equation of chord with given middle point  $T=S_1$
 $$\begin{gathered} \frac{x}{25}+\frac{y}{40}=\frac{1}{25}+\frac{1}{100} \\ \frac{8x+5y}{200}=\frac{8+2}{200} \end{gathered}$$
 $y=\frac{10-8x}{5}$                                     ….. (i)