Question

Find the equation of the circle whose centre is same as the centre of the circle x2 + y2 + 6x + 2y + 1 = 0, and passing through the point (-2, -3).

Answer 1

Given x2 + y2 + 6x + 2y + 1 = 0, P = (-2,-3)

Centre = C(-3,-1),

Let the equations of the required circle is x2 + y2 + 6x + 2y + C = 0 r = CP

= (\sqrt{(-2 + 3)^2 + (-3 + 1)^2} = \sqrt{1^2 + 0} = 1)

∴ r = (\sqrt{g^2 + f^2 - c})

I = (\sqrt{9 + 1 - c})

⇒ 1 = 10 - c ⇒ c = 9

∴ The required equation of the circle is

x2 + y2 + 6x + 2y + 9 = 0.