A circle is concentric with the circle $x^{2} + y^{2} - 6 x + 12 y + 15 = 0$ and has area double of its area. The equation of the circle is

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Solution

The correct option is A
Equation of circle concentric to given circle is $x^{2} + y^{2} - 6 x + 12 y + k = 0 \dots \dots \dots (i)$
Radius of circle (i) = $\sqrt{2}$ (radius of given circle)
$\Rightarrow \sqrt{9 + 36 - k} = \sqrt{2} \sqrt{9 + 36 - 15}$
$\Rightarrow 45 - k = 60 \Rightarrow k = - 15$
Hence the required equation of circle is
$x^{2} + y^{2} - 6 x + 12 y - 15 = 0$

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