Two circles, each of radius , have a common tangent at whose equation is then their centers are
,
Explanation for the correct answer:
Let be the center of one of the circle
The line joining to will be perpendicular to the common tangent
Let be the slope of the tangent
Let be the slope of line joining to .
is also given as
Also the distance between center and is equal to the radius
…(from )
or
Re-substituting these values in we get,
or
or
Therefore, the co-ordinates of the center are and .
Hence, option (C) is the correct answer.