Find the equation of the circle concentric with the circle x2 + y2 + 4x + 6y + 11 = 0 and passing through the point P(5, 4).

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



Given, x2 + y2 + 4x + 6y + 11 = 0


The concentric circle will have the equation


x2 + y2 + 4x + 6y + c’ = 0


As it passes through P(5, 4), putting this in the equation


52 + 42 + 45 + 64 + c’ = 0


25 + 16 + 20 + 24 + c’ = 0


c’ = - 85


The required equation is


x2 + y2 + 4x + 6y - 85 = 0


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