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

Question

Accepted Answer

Correct answer: C. (c) Circle 1: center (0 ,0 ) ,r=2. Circle 2: centre (0 ,2 ) ,r=2. Distance between centers 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 = 12 (4 ) ( 2 3 )- 12 (4 ) sin ⁡ 2 3= 4 3- 3. By symmetry, total intersection area =2( 4 3- 3)= 8 -6 33= 23 (4 -3 3 ).

$The area of the region enclosed between the circles x^{2} + y^{2} = 4 and x^{2} + (y - 2)^{2} = 4 is:$

Solution

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