JEE Math Practice Question

Let $$e_1$$ be the eccentricity of the hyperbola $$\frac{x^2}{16}-\frac{y^2}{9}=1$$ and $$e_2$$ be the eccentricity of the ellipse $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, \mathrm{a} > \mathrm{b}$$, which passes through the foci of the hyperbola. If $$\mathrm{e}_1 \mathrm{e}_2=1$$, then the length of the chord of the ellipse parallel to the $$x$$-axis and passing through $$(0,2)$$ is :

1. A.$$\frac{8 \sqrt{5}}{3}$$
2. B.$$3 \sqrt{5}$$
3. C.$$4 \sqrt{5}$$
4. D.$$\frac{10 \sqrt{5}}{3}$$