The area bounded by the circles `x^2+y^2=1,x^2+y^2=4,` and the pair of lines `sqrt(3)(x^2+y^2)=4x y` is equal to `pi/2` (b) `(5pi)/2` (c) `3pi` (d) `pi/4`

Options

A. `pi //2`
B. `5pi//2`
C. `3pi`
D. `pi//4`

Answer

4

Explanation

The angle `theta` between the lines represented by
`sqrt(3)x^(2)-4xy+sqrt(3)y^(2)=0` is given by
`theta=tan^(-1).(sqrt(h^(2)-ab))/(|a+b|)`
`=tan^(-1).(2sqrt(2^(2)-3))/(sqrt(3)+sqrt(3))=(pi)/(6)`
Hence, the shaded area is
`(pi//6)/(2pi)xxpi(2^(2)-1^(2))=(pi)/(4)`