## Book: RD Sharma - Mathematics (Volume 2)

### Chapter: 21. Areas of Bounded Regions

#### Subject: Maths - Class 12th

##### Q. No. 42 of Exercise 21.3

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42
##### Find the area of the region enclosed between the two curves x2 + y2 = 9 and (x – 3)2 + y2 = 9.

To find area enclosed by

X2 + y2 = 9 (i)

(x – 3)2 + y2 = 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 x2 + y2 = 9 and (x – 3)2 + y2 = 9 is

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