A circle touches both the coordinate axes and the line `x-y=sqrt(2)a, a gt 0`, the coordinates of the centre of the circle cannot be

Options

A. (a, a)
B. (a, -a)
C. (-a, a)
D. (-a, -a)

Answer

B

Explanation

Let the radius of the circle be r. Then, coordinates of its centre can be (r, r), (-r, -r) and (r, -r).

The circle touches `x-y=sqrt(2)a`
`:. |(-sqrt(2)a)/(sqrt(2))|=r` when centre is at (r, r) or (-r, -r)
and `|(2r-sqrt(2)a)/(sqrt(2))|=r` when centre is at (r, -r)
`rArr r=a and r=(sqrt(2) pm 1)a`