2. A line with a slope of $\frac{2}{21} \sqrt{21}$ passing through the foci of the hyperbola $16 x^{2}-9 y^{2}=144$ intersects the hyperbola. Find the length of the chord intercepted.
2. The hyperbola equation is transformed to $\frac{y^{2}}{16}-\frac{x^{2}}{9}=1$, with the foci on the $y$-axis, $a=4, b=3, c=5, e=\frac{5}{4}, e p=\frac{9}{4}$, slope $k^{\prime}=$ $\frac{2}{21} \sqrt{21}$, taking $k=\frac{1}{k^{\prime}}=\frac{\sqrt{21}}{2}$. From property 2, we find $l=\frac{2 e p\left(1+k^{2}\right)}{\left(1+k^{2}\right)-e^{2}}=6$.