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

### Chapter: 21. Areas of Bounded Regions

#### Subject: Maths - Class 12th

##### Q. No. 17 of Exercise 21.3

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

17
##### Prove that the area in the first quadrant enclosed by the axis, the line x = √3y and the circle x2 + y2 = 4 is π/3.

To find an area in the first quadrant enclosed by the x – axis,

x = √3y

x2 + y2 = 4

Or

Or

Or

And

Equation (i) represents a line passing through (0,0), ( – √3, – 1), (√3,1).

Equation (ii) represents a circle centre (0,0) and passing through (±2,0), (0,±2).

Points of intersection of line and circle are ( – √3, – 1) and (√3,1).

These are shown in the graph below: -

Required enclosed area = Region OABO

= Region OCBO + Region ABCA

Hence proved that the area in the first quadrant enclosed by the axis, the line and the circle is π/3.

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