RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 21. Areas of Bounded Regions

Subject: Maths - Class 12th

Q. No. 42 of Exercise 21.3

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

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


Chapter Exercises

More Exercise Questions