Question

Find the area of the region enclosed b/w the two circles. x² + y² = 4 and (x - 2)² + y² = 4

Answer 1

Equations of the given circles are 

x² + y² = 4  ……….. (1)

(x - 2)² + y² = 4 ………….(2)

Equation (1) is a circle with centre O at the origin and radius 2. 

Eqn. (2) is a circle with centre C (2, 0) and radius 2. Solving Eqn. 

(1) and (2), we have. 

(x - 2 )² + y² = x² + y² 

x² – 4x + 4 + y² = x² + y² + 4x = -4 

⇒ x = 1 x = 1 which given y = ± √3 

Thus the points of intersection of the given circles are A(1,√3) and A¹(1,-√3) as shown in the fig. 

Required area of the enclosed region OACA¹O between circles

= 2 [area of the region ODCAO] 

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