ExamBro
ExamBro
TS EAMCET · Maths · Area Under Curves

The area (in square units) of the region enclosed by the two circles \(x^2+y^2=1\) and \((x-1)^2+y^2=1\) is

  1. A \(\frac{2 \pi}{3}+\frac{\sqrt{3}}{2}\)
  2. B \(\frac{\pi}{3}+\frac{\sqrt{3}}{2}\)
  3. C \(\frac{\pi}{3}-\frac{\sqrt{3}}{2}\)
  4. D \(\frac{2 \pi}{3}-\frac{\sqrt{3}}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{2 \pi}{3}-\frac{\sqrt{3}}{2}\)

Step-by-step Solution

Detailed explanation

Intersection point of two circles \(x^2+y^2=1\) \(\ldots\) (i) \((x-1)^2+y^2=1\) \(\ldots\) (ii) is given by \((x-1)^2+\left(1-x^2\right)=1\) \(\Rightarrow \quad x^2+1-2 x-x^2=0\) \(\Rightarrow \quad x=\frac{1}{2}\) From Eq. (i), \(\frac{1}{4}+y^2=1\)…