Let P(2√3/√7 , 6/√7), QR and S be four points on the ellipse 9x^2 + 4y^2 = 36.

Question

Let P\(\left(\frac{2\sqrt{3}}{\sqrt{7}},\frac{6}{\sqrt{7}}\right)\), QR and S be four points on the ellipse 9x² + 4y² = 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 

(1) 143 

(2) 137 

(3) 157 

(4) 147

Answer 1

Correct option is (3) 157

Let R(2cosθ, 3sinθ) 

as OP⟂OR