# Find the area of the region between circles x2 + y2 = 4 and (x – 2)2 + y2 = 4. [CBSE 2012, 2013]

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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Fundamental Integration Formula59 mins
Application of Biotechnology48 mins
Interactive Quiz on Integration by Substitution47 mins
Lecture on Integration by parts55 mins
Lecture on some forms of integration54 mins
Lecture on integration by partial fractions62 mins
Interactive Quiz on Integration by Parts56 mins
Integration by Substitution56 mins
How to find Maxima & Minima?43 mins
Tangent & Normal To A Curve53 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses