Question
The area of the region enclosed between the circles x^ 2 +y^ 2 =4 and x^ 2 +(y-2)^ 2 =4 is:
JEE Main
Mathematics
Area Under Curves
2026
JEE Main 2026 (23 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 4 3 (2 -3 3 )
- B. 2 3 (2 -3 3 )
- C. 2 3 (4 -3 3 )
- D. 4 3 (2 - 3 )
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 ).
Related: Mathematics — Area Under Curves · All PYQ Banks