jee-main 2024 Q66

jee-main · India · session1_30jan_shift2 Circles Circle Equation Derivation

Let $A(\alpha, 0)$ and $B(0, \beta)$ be the points on the line $5x + 7y = 50$. 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 $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ 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
(1) $\frac{25}{3}$
(2) $\frac{32}{9}$
(3) $\frac{25}{9}$
(4) $\frac{32}{5}$

Let $A(\alpha, 0)$ and $B(0, \beta)$ be the points on the line $5x + 7y = 50$. 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 $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ 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\\
(1) $\frac{25}{3}$\\
(2) $\frac{32}{9}$\\
(3) $\frac{25}{9}$\\
(4) $\frac{32}{5}$

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