The equation $x^{2} + y^{2} - 2 x + 4 y + 5 = 0$ represents

a point

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a pair of straight lines

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a circle of non zero radius

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none of these

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Solution

The correct option is B a point
$x^{2} + y^{2} - 2 x + 4 y + 5 = 0$
$(x - 1)^{2} + (y + 2)^{2} - 5 + 5 = 0$
$\Rightarrow (x - 1)^{2} + (y + 2)^{2} = 0$
Since, radius is $0$ , hence its a point
Alternative method:
Here, $a = b = 1$
$r = \sqrt{1 + 4 - 5} = 0$
Hence, a circle of radius $0$ . So, its a point.

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