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

### Chapter: 21. Areas of Bounded Regions

#### Subject: Maths - Class 12th

##### Q. No. 11 of Exercise 21.3

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

11
##### Find the area of the region between circles x2 + y2 = 4 and (x – 2)2 + y2 = 4.

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

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52