Given $c_{1} : x^{2} + y^{2} - 2 x - 2 y + 3 = 0$ and $c_{2} : x^{2} - y^{2} - 2 x - 2 y + 7 = 0$ are

concentric circles

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similar circles

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congruent circles

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none of these

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Solution

The correct option is A none of these
The equation of $c_{1}$ is $(x - 1)^{2} + (y - 1)^{2} + 1 = 0$
The equation of $c_{2}$ is $(x - 1)^{2} - (y + 1)^{2} + 7 = 0$
Observe that $c_{2}$ is not the equation of circle as $y^{2}$ is in negative.
So the correct answer is none of these (option $D$ )

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Similar questions

C_{1} : x^{2} + y^{2} + 2 x - 3 = 0, C_{2} : x^{2} + y^{2} - 2 x - 3 = 0, C_{3} : x^{2} + y^{2} - 2 y - 3 = 0,

C_{1} : x^{2} + y^{2} - 2 x - 4 y - 4 = 0

C_{2} : x^{2} + y^{2} + 2 x + 4 y + 4 = 0

L : x + 2 y + 2 = 0,

x^{2} + y^{2} + 2 x - 2 y + 1 = 0 a n d x^{2} + y^{2} - 2 x - 2 y + 1 = 0

x^{2} + y^{2} = 1, x^{2} + y^{2} - 2 x - 3 = 0

x^{2} + y^{2} - 2 y - 3 = 0

x^{2} + y^{2} - 2 x - 1 = 0

x^{2} + y^{2} - 2 y - 7 = 0

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