Mathematics Question from JEE Main 2024 · 27 January, Shift 2

If $e_1$ is the eccentricity of the hyperbola $\frac{x^2}{16} - \frac{y^2}{9} = 1$ and $e_2$ is the eccentricity of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, which passes through the foci of the hyperbola and satisfies $e_1e_2 = 1$, then the length of the chord of the ellipse parallel to the $x$-axis and passing through $\left(0,2\right)$ is: