Normal to the circle `x^(2)+y^(2)=4` divides the circle having centre at (2,4) and radius 2 in the ares of ratio `(pi -2) : (3pi +2)`. Then the normal can be

Options

A. `y=x`
B. `y= 3x`
C. `y=5x`
D. `y=7x`

Answer

1,4

Explanation

Normal to the circles `x^(2)+y^(2)=4 ` passes through its centre (0,0)

So, equation of normal is `y= mx`.
Now, according to the question.
`("Area of regio ADBA")/("Area of regioN abefa")=(pi-2)/(23pi+2)`
`:. ([(pi(2)^(2))/(2pi).theta-(1)/(2)(2)^(2)sin theta])/(pi(2)^(2)-[(pi(2)^(2))/(2pi).theta-(1)/(2)(2)^(2)sin theta])=(pi-2)/(3pi+2)`
`implies theta =(pi)/(2)`
`:. `Distance of centre of circle from line `= 2 cos. (pi)/(4)`
`implies (|4-2m|)/(sqrt(1+m^(2)))=sqrt(2)`
`implies m =1,7`