Let $x=\frac{m}{n}$ ($m, n$ are co-prime natural numbers) be a solution of the equation $\cos \left(2 \sin ^{-1} x\right)=\frac{1}{9}$ and let $\alpha, \beta(\alpha >\beta)$ be the roots of the equation $m x^2-n x-m+ n=0$. Then the point $(\alpha, \beta)$ lies on the line