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The circle passing through the intersection of the circles , $x^{2} + y^{2} - 6 x = 0$ and $x^{2} + y^{2} - 4 y = 0,$ having its centre on the line, $2 x - 3 y + 12 = 0$ , also passes through the point

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$(- 3, 1)$

$(1, - 3)$

$(- 1, 3)$

$(- 3, 6)$

answer is D.

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Detailed Solution

$L = s - s^{1} = 0$
The center of $S + λ L = 0$
Lies on the line $2 x - 3 y + 12 = 0$

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