Let $a, b\in \mathbf{R}^+, \lambda >1$. $\Omega: \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$, Point $M(\dfrac a{\lambda}, 0), A(-a,0),B(a, 0)$. Let line $l$ pass through $M$ and intersect with $\Omega$ at points $P$ and $Q$. ($P$ is above the $X$-axis while $Q$ is below it). I found that $\dfrac{k\_{QB}}{k\_{PA}}=\dfrac{\lambda+1}{\lambda-1}$, but cannot prove it.

I tried to prove it in a circle first, but the calculation is just too complex for me to handle.

[GeoGebra link to the problem](https://www.geogebra.org/calculator/ha93qde2)