If the circle  and  touches each other then the maximum value of ‘’ is

(1)

   (1)

  (2)

Since both the circles are passing through the origin (0, 0), equation of tangent at (0,0) will be same tangent at (0,0) to circle (1),

   (3)

Tangent at (0, 0) to circle (2),

 (1) and (2) must be identical

comparing (1) and (2)

 when  and