Hyperbola

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 :