If the midpoint of a chord of the ellipse $\frac{{\mathrm{x}}^2}{16}+\frac{{\mathrm{y}}^2}{25}=1$ 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) is $\frac{3y}{25}-1=\frac{9}{25}-1$
i.e., y = 3
It intersects the ellipse $\frac{{\mathrm{x}}^2}{16}+\frac{{\mathrm{y}}^2}{25}=1\text{ at }\frac{{\mathrm{x}}^2}{16}=1-\frac{9}{25}=\frac{16}{25}\text{ or }\mathrm{x}=\pm \frac{16}{5}$
$\therefore$length of chord $=\frac{32}{5}\text{ Thus, }\frac{4\mathrm{k}}{5}=\frac{32}{5}\therefore \mathrm{k}=8$