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Let P((2sqrt3)/(sqrt7),6/(sqrt7)),Q,R,an...

Let `P((2sqrt3)/(sqrt7),6/(sqrt7))`,Q,R,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 `1/((PQ)^2+1/(RS)^2)=p/q, `where p and q are coprime , then `p+q` is equal to

A

`147`

B

`157`

C

`137`

D

`143`

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