3. Given that the length of the major axis of an ellipse is 4, the focal distance is 2, and the sum of the lengths of two perpendicular chords passing through the left focus is $\frac{48}{7}$. Try to find the product of the lengths of these two chords.

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3. Let the lengths of the two chords be $m, n$. Given $a=2, c=1$, then $b^{2}=3$. By property 11 (II), we know $\frac{2}{2}\left(\frac{1}{m}+\frac{1}{n}\right)=\frac{1}{4}+$ $\frac{1}{3}$, so $m n=\frac{12}{7}(m+n)=\frac{12}{7} \cdot \frac{48}{7}=\frac{576}{49}$.