Find the area of the region enclosed between the two curves x^{2} + y^{2} = 9 and (x – 3)^{2} + y^{2} = 9.

To find area enclosed by

X^{2} + y^{2} = 9 (i)

(x – 3)^{2} + y^{2} = 9 (ii)

On solving equation (i) and (ii) we get,

X = and y = ±

Equation (i) represents a circle with centre (0,0) and meets axes at (±3,0),(0,±3).

Equation (ii) is a circle with centre (3,0) and meets axe at (0,0), (6,0).

They intersect each other at and .

These are shown in the graph below:

Required area = Region OABCO

= 2(Region OBCO)

= 2(Region ODCO + Region DBCD)

The area of the region enclosed between the two curves curves x^{2} + y^{2} = 9 and (x – 3)^{2} + y^{2} = 9 is

42