Find the equation of the circle concentric with the circle x2 + y2 – 6x + 12y + 15 = 0 and of double its area.

2 or more circles are said to be concentric if they have the same centre and different radii.


Given, x2 + y2 - 6x + 12y + 15 = 0


Radius r =


The concentric circle will have the equation


x2 + y2 - 6x + 12y + c’ = 0


Also given area of circle = 2area of the given circle.


r’2 = 2r2 = 230 = 60


We can get c’ = 45 - 60 = - 15


The required equation is x2 + y2 - 6x + 12y - 15 = 0.


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