Question

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

Answer 1

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 + 4 x 5 + 6x 4 + c = 0

25 + 16 + 20 + 24 + c = 0

c = -85

The required equation is 

x² + y² + 4x + 6y - 85 = 0