The equation of a circle of radius 1 touching the circles `x^2+y^2-2|x|=0` is (a) `x^2+y^2+2sqrt(2)x+1=0` (b) `x^2+y^2-2sqrt(3)y+2=0` (c) `x^2+y^2+2sqrt(3)y+2=0` (d) `x^2+y^2-2sqrt(2)+1=0`

Options

A. `x^(2)+y^(2)+2sqrt(2)x+1=0`
B. `x^(2)+y^(2)-2sqrt(3)y+2=0`
C. `x^(2)+y^(2)+2sqrt(3)y+2=0`
D. `x^(2)+y^(2)-2sqrt(2)+1=0`

Answer

2,3

Explanation

The given circles are `x^(2)+y^(2)-2x=0,x gt 0`, and `x^(2)+y^(2)+2x=0, x lt 0`. From the figure, the centers of the required circles will be `( 0, sqrt(3))` and `(0, - sqrt(3))`.
Therefore, the equations of the circles are
`(x-0)^(2)+(y+- sqrt(3))^(2) =1^(2)`