If a straight line y-x=2 divides the region x^2+y^2 4 into two parts, then the ratio of the area of the smaller part to the area of the greater part is

Step-by-step solution

Let I be the smaller portion and II be the greater portion of the given figure then, Area of I= _ -2 ^0 [ 4-x^2 -(x+2] d x . aligned & = [ x 2 4-x^2 + 4 2 ⁻¹ ( x 2 ) ]_ -2 ^0- [ x^2 2 +2 x ]_ -2 ^0 & = [2 ⁻¹(-1) ]- [- 4 2 +4 ]=2 2 -2= -2 aligned Now, area of II = Area of circle - area of I . aligned & =4 -( -2) & =3 +2 aligned Hence, required ratio = area of I area of II = -2 3 +2