Coordinate Geometry: JEE Main 2024 Mathematics 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 :