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JEE Main202623 January 2026Evening ShiftMathematicsArea Under CurvesActual

The area of the region enclosed between the circles x²+y²=4 and x²+(y-2)²=4 is:

Options

  1. A4 3 (2 -3 3 )
  2. B2 3 (2 -3 3 )
  3. C2 3 (4 -3 3 )
  4. D4 3 (2 - 3 )

Correct answer

C. 2 3 (4 -3 3 )

Step-by-step solution

Circle 1: centre (0,0) , r=2 . Circle 2: centre (0,2) , r=2 . Distance between centres d=2 . Intersection: y^2 = (y-2)^2 y = 1 , giving x = 3 . Angle subtended at centre of circle 1 by the chord: = 2 /3 . Segment area = 1 2 (4) ( 2 3 ) - 1 2 (4) 2 3 = 4 3 - 3 . By symmetry, total intersection area = 2 ( 4 3 - 3 ) = 8 - 6 3 3 = 2 3 (4 - 3 3 ) .

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