Let x=m/n ( m, n are co-prime natural numbers) be a solution of the equation cos (2 sin^-1 x)=1/9 and let α, β(α>β) be the roots of the equation m…

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