Author: mathsindeep@gmail.com

The parabola \(y^2=4 x\) divides the area of the circle \(x^2+y^2=5\) in two parts. The area of the smaller part is equal to : (A) \(\frac{2}{3}+5 \sin ^{-1}\left(\frac{2}{\sqrt{5}}\right)\) (B) \(\frac{1}{3}+5 \sin ^{-1}\left(\frac{2}{\sqrt{5}}\right)\) (C) \(\frac{2}{3}+\sqrt{5} \sin ^{-1}\left(\frac{2}{\sqrt{5}}\right)\) (D) \(\frac{1}{3}+\sqrt{5} \sin ^{-1}\left(\frac{2}{\sqrt{5}}\right)\)