Problem 9.7. Two parallel lines are drawn through points $A(0 ; 14)$ and $B(0 ; 4)$. The first line, passing through point $A$, intersects the hyperbola $y=\frac{1}{x}$ at points $K$ and $L$. The second line, passing through point $B$, intersects the hyperbola $y=\frac{1}{x}$ at points $M$ and $N$.

What is $\frac{A L-A K}{B N-B M}$ ?

![](https://cdn.mathpix.com/cropped/2024_05_06_d43b1f0a7bd77fffa87ag-31.jpg?height=525&width=519&top_left_y=488&top_left_x=467)