Let \( x = \dfrac{m}{n} \) (\( m, n \) are co-prime natural numbers) be a solution of the equation \( \cos (2 \sin^{-1} x )= \dfrac{1}{9} \) 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.
