The coordinates of the centre of the circle $x^{2} + 2 y^{2} + 2 x = 0$ is:

(- 1, 0)

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(- 1, 1)

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(1, 0)

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(1, - 1)

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Solution

The correct option is A $(- 1, 0)$
Given the equation of the ellipse,
$x^{2} + 2 y^{2} + 2 x = 0$
or, $x^{2} + 2 x + 1 + y^{2} = 1$
or, $(x + 1)^{2} + y^{2} = 1$ .
From the equation of the circle we've the centre is $(- 1, 0)$ .

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What are the coordinates of the centre of the circle $x^{2} + y^{2} - 2 x - 2 y + 1 = 0$ .

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