Let P( 2√3/√7, 6/√7), Q, R, and S be four points on the ellipse 9… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 12 April, Shift 1Conic Sections (Parabola, Ellipse, Hyperbola)

Let $P\left( \frac{2\sqrt{3}}{\sqrt{7}}, \frac{6}{\sqrt{7}} \right), Q, R, \text{ and } S$ be four points on the ellipse $9x^2 + 4y^2 = 36$ . Let $PQ$ and $RS$ be mutually perpendicular and pass through the origin. If

\frac{1}{(PQ)^2} + \frac{1}{(RS)^2} = \frac{p}{q}

where $p$ and $q$ are coprime, then $p + q$ is equal to:

A
$143$
B
$137$
C
$157$
D
$147$

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