The radius of the circle $x^{2} + y^{2} + 4 x - 6 y - 12 = 0$ is

9

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5

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- 3

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Solution

The correct option is B $5$
Equation of the circle is $x^{2} + y^{2} + 4 x - 6 y - 12 = 0.$
We know that Standard equation of the circle is $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$
Comparing the given equation with the standard equation,
we get $g = 2, f = - 3$ and $c = - 12.$
We also know that the radius of the circle $= \sqrt{g^{2} + f^{2} - c} = \sqrt{{(2)}^{2} + {(- 3)}^{2} + 12} = \sqrt{25} = 5.$

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