jee-main 2023 Q71

jee-main · India · session2_12apr_shift1 Conic sections Chord Properties and Midpoint Problems

Let $P \left( \frac { 2 \sqrt { 3 } } { \sqrt { 7 } } , \frac { 6 } { \sqrt { 7 } } \right) , Q , R$ and $S$ be four points on the ellipse $9 x ^ { 2 } + 4 y ^ { 2 } = 36$. Let $P Q$ and $R S$ be mutually perpendicular and pass through the origin. If $\frac { 1 } { ( P Q ) ^ { 2 } } + \frac { 1 } { ( R S ) ^ { 2 } } = \frac { p } { q }$, where $p$ and $q$ are coprime, then $p + q$ is equal to
(1) 147
(2) 143
(3) 137
(4) 157

Let $P \left( \frac { 2 \sqrt { 3 } } { \sqrt { 7 } } , \frac { 6 } { \sqrt { 7 } } \right) , Q , R$ and $S$ be four points on the ellipse $9 x ^ { 2 } + 4 y ^ { 2 } = 36$. Let $P Q$ and $R S$ be mutually perpendicular and pass through the origin. If $\frac { 1 } { ( P Q ) ^ { 2 } } + \frac { 1 } { ( R S ) ^ { 2 } } = \frac { p } { q }$, where $p$ and $q$ are coprime, then $p + q$ is equal to\\
(1) 147\\
(2) 143\\
(3) 137\\
(4) 157

Paper Questions

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