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Let x 2 + y 2 = 4 r 2 and x y = 1 intersects at A and B in first quadrant. If A B = 14 units, then the value of r is

Correct answer

1.5

Step-by-step solution

Let A = t , 1 t & B = 1 t , t ∵ B o t h c u r v e s a r e s y m m e t r i c a b o u t l i n e 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 ⇒ 2 r 2 = 9 ⇒ 2 r = 3 ⇒ r = 1.5

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