jee-main 2024 Q67

jee-main · India · session1_01feb_shift2 Conic sections Locus and Trajectory Derivation

Let $P$ be a point on the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$. Let the line passing through $P$ and parallel to $y$-axis meet the circle $x^2 + y^2 = 9$ at point $Q$ such that $P$ and $Q$ are on the same side of the $x$-axis. Then, the eccentricity of the locus of the point $R$ on $PQ$ such that $PR:RQ = 4:3$ as $P$ moves on the ellipse, is:
(1) $\frac{11}{19}$
(2) $\frac{13}{21}$
(3) $\frac{\sqrt{139}}{23}$
(4) $\frac{\sqrt{13}}{7}$

Let $P$ be a point on the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$. Let the line passing through $P$ and parallel to $y$-axis meet the circle $x^2 + y^2 = 9$ at point $Q$ such that $P$ and $Q$ are on the same side of the $x$-axis. Then, the eccentricity of the locus of the point $R$ on $PQ$ such that $PR:RQ = 4:3$ as $P$ moves on the ellipse, is:\\
(1) $\frac{11}{19}$\\
(2) $\frac{13}{21}$\\
(3) $\frac{\sqrt{139}}{23}$\\
(4) $\frac{\sqrt{13}}{7}$

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