Let A(10, 0) and B(0, β) be points on the line 5x + 7y = 50. Let… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 30 January, Shift 2Conic Sections (Parabola, Ellipse, Hyperbola)

Let $A(10, 0)$ and $B(0, \beta)$ be points on the line $5x + 7y = 50$ . Let $P$ divide $AB$ in the ratio $7:3$ . Let $3x-25 = 0$ be a directrix of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ , and focus $S$ such that a perpendicular from $S$ passes through $P$ . Find the length of the latus rectum:

A
$\frac{25}{3}$
B
$\frac{32}{9}$
C
$\frac{25}{9}$
D
$\frac{32}{5}$

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