If the midpoint of a chord of the ellipse $\frac{x^2}{16}+\frac{y^2}{25}=1$is $(0,3)$and the length of the chord is $4k/5$, then $k$is ______________

The equation of the chord whose midpoint is $(0,3)$ $\frac{3y}{25}-1=\frac{9}{25}-1$

$i.e.,y=3$

It intersects the ellipse

$\frac{x^2}{16}+\frac{y^2}{25}=1$

$\frac{x^2}{16}=1-\frac{9}{25}=\frac{16}{25}orx=\pm \frac{16}{5}$

$\text{Length of chord}=\frac{32}{5}$

Thus,$\frac{4k}{5}=\frac{32}{5}\Rightarrow \therefore k=8$