Let a , β be an ordered pair of real numbers satisfying the equation x 2 - 4 x + 4 y 2 + 3 = 0 . If the maximum and minimum values of a 2 + β 2 are l and s respectively, then the value of l - s l + s is equal to

Question

Let a , β be an ordered pair of real numbers satisfying the equation x 2 - 4 x + 4 y 2 + 3 = 0 . If the maximum and minimum values of a 2 + β 2 are l and s respectively, then the value of l - s l + s is equal to,

MARKS App · Accepted Answer

a 2 + β 2 represents the distance of a , β from the origin 0,0 . Now, let the line joining O 0 , 0 and center of circle C 2,0 cuts the circle at points 1,0 = A and 3,0 = B , then, l = O B = 3 and s = O A = 1 ⇒ l - s l + s = 2 4 = 0 . 5

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