$\text{ If the mid point of a chord of the ellipse }\frac{x^2}{16}+\frac{y^2}{25}=1\text{ is }(0,3)\text{ , then length of the chord is}$

$\text{ Equation of the chord whose mid point is }(0,3)\text{ is }$

$\begin{array}{l}\frac{3y}{25}-1=\frac{9}{25}-1\text{ i.e. }y=3\\ \text{ It intersects the ellipse }\frac{x^2}{16}+\frac{y^2}{25}=1\text{ at }\end{array}$

$\begin{array}{l}\frac{x^2}{16}=1-\frac{9}{25}=\frac{16}{25}\\ \Rightarrow x=\pm \frac{16}{5}\\ \therefore \text{ length of the chord }=\frac{32}{5}\end{array}$