Find the equation of the circle whose centre is same as the centre of

1.	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» 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.

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»

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.

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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).

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