If the equation `lamdax^(2)+(2lamda-3)y^(2)-4x-1=0` represents a circle, then its radius is

Options

A. `(sqrt(11))/(3)`
B. `(sqrt(13))/(3)`
C. `(sqrt(7))/(3)`
D. `(1)/(3)`

Answer

C

Explanation

Given equation is
`lamdax^(2)+(2lamda-3)y^(2)-4x-1=0`
here, a=`lamda,b=(2lamda-3)`
It represents a circle, if a=b.
`implieslamda=2lamda-3`
`thereforelamda=3`
Then, equation becomes
`3x^(2)+3y^(2)-4x-1=0`
`impliesx^(2)+y^(2)-(4)/(3)x-(1)/(3)=0`
Here, `g=-(2)/(3),c=-(1)/(3),f=0`
`therefore` Radius
`=sqrt((-(2)/(3))^(2)+0-(-(1)/(3)))`
`=sqrt((4)/(9)+(1)/(3)))`
`=(sqrt(7))/(3)`