The equation of the circle with centre at (1, -2) and passing through the centre of the given circle $x^{2} + y^{2} + 2 y - 3 = 0,$ is

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Solution

The correct option is A
According to the question, the required circle passes through (0, -1). Therefore, the radius is the distance between the points (0, -1) and (1, -2) i.e., $\sqrt{2} .$
Hence the equation is $(x - 1)^{2} + (y + 2)^{2} = {(\sqrt{2})}^{2}$
$\Rightarrow x^{2} + y^{2} - 2 x + 4 y + 3 = 0$
Trick: Since this is the only circle passing through (0, -1).

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The equation of the circle with centre at (1, -2) and passing through the centre of the given circle x2+y2+2y−3=0, is

The equation of the circle with centre at (1, -2) and passing through the centre of the given circle $x^{2} + y^{2} + 2 y - 3 = 0,$ is