Q. 95.0( 2 Votes )

Find the area of

Answer :

The given equations are,


x2 + y2 = 4 ...(i)


(x – 2)2 + y2 = 4 ...(ii)


Equation (i) is a circle with centre O at origin and radius 2.


Equation (ii) is a circle with centre C (2,0) and radius 2.


On solving these two equations, we have


(x – 2)2 + y2 = x2 + y2


Or x2 – 4x + 4 + y2 = x2 + y2


Or x = 1 which gives y ± √3


Thus, the points of intersection of the given circles are A (1, √3) and A’ (1, – √3) as show in the graph below



Now the bounded area is the required area to be calculated, Hence,


Required area of the enclosed region OACA’O between circle


A = [area of the region ODCAO]


= 2 [area of the region ODAO + area of the region DCAD]










The area of the region between circles x2 + y2 = 4 and (x – 2)2 + y2 = 4 is

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