Question

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

Answer 1

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 = \(\sqrt{g^2+f^2-c}=\sqrt{(-3^2)+6^2-15}\) = \(\sqrt{30}\)

The concentric circle will have the equation

 x² + y² - 6x + 12y + c’ = 0

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

r'² = 2 x r² = 2 x 30 = 60

We can get C' = 45 - 60 = -15

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