Let x 2 + y 2 = r 2 and x y = 1 intersect at A and B in the first quadrant. If A B = 14 units, then the square of the distance of A B from the origin is equal to

Question

Let x 2 + y 2 = r 2 and x y = 1 intersect at A and B in the first quadrant. If A B = 14 units, then the square of the distance of A B from the origin is equal to,

MARKS App · Accepted Answer

Let, A = t , 1 t and B = 1 t , t { ∵ both curves are symmetric about line y = x } Then, A B 2 = t - 1 t 2 + 1 t - t 2 = 14 ⇒ 2 t 2 + 1 t 2 = 14 + 4 ⇒ t 2 + 1 t 2 = 9 Now, O A 2 = t 2 + 1 t 2 = 9 ⇒ r 2 = 9 ⇒ r = 3 ⇒ O F 2 = 9 - 14 4 = 5.5

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