Let \( A(\alpha, 0) \) and \( B(0, \beta) \) be the points on the line. Let the point \( P \) divide the line segment \( AB \) internally in the ratio \( 7:3 \). Let \( 3x - 25 = 0 \) be a directrix of the ellipse \( E: \, \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 \) and the corresponding focus be \( S \). If from \( S \), the perpendicular on the \( x \)-axis passes through \( P \), then the length of the latus rectum of \( E \) is equal to:
