Co-ordinates of the centre of a circle, whose radius is 2 unit and which touches the pair of lines `x^2-y^2-2x + 1 = 0` is (are)

Options

A. `(4,0)`
B. `(1+2sqrt(2),0)`
C. `(4,1)`
D. `(1,2sqrt(2))`

Answer

2,4

Explanation

Line pair `(x-1)^(2)-y^(2)=0, i.e., x+y-1 =0` and `x-y-1=0`. Let the center be `(alpha,0)`. Then its distance from `x+y-1=0` is
`|(alpha-1)/(sqrt(2))|=2 ` (radius)
`i.e., alpha =1 +- 2sqrt(2)`
So, the center may be `(1+2sqrt(2),0),(1-2sqrt(2),0)`.
Now, let the center be `(1, beta)`. Then,
`|(1+beta+1)/(sqrt(2))|=2`
or `beta = +-2sqrt(2)`
So, the centre may be `(1,2sqrt(2)),(1,-2sqrt(2))`