QJEEM24Maddac: JEE Main 2024 Mathematics - Class 11 JEEM24Maddac Solution: Let and be the points on the line . Let the point divide the…

Let $A(\alpha, 0)$ and $B(0, \beta)$ be the points on the line $5 x+7 y=50$ . Let the point $P$ divide the line segment $A B$ internally in the ratio $7:3$ . Let $3 x-25=0$ be a directrix of the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ 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,