The point of contact of the circle $x^{2} + y^{2} + 2 x + 2 y + 1 = 0$ and $x^{2} + y^{2} - 2 x + 2 y + 1 = 0$ is

(0, 1)

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(0, -1)

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(1, 0)

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(-1, 0)

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Solution

The correct option is B (0, -1)
$x^{2} + y^{2} + 2 x + 2 y + 1 = 0$ ..........(1)
$x^{2} + y^{2} - 2 x + 2 y + 1 = 0$ .........(2)
Subtract (2) from (1)
$\Rightarrow 4 x = 0 \Rightarrow x = 0$
Substitute in (1) $\Rightarrow y^{2} + 2 y + 1 = 0$
$\Rightarrow (y + 1)^{2} = 0 \Rightarrow y = - 1$
Hence required point is $(0, - 1)$

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