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If $4 l^{2} - 5 m^{2} + 6 l + 1 = 0$ then the line $l x + m y + 1 = 0$ touches a fixed circle whose centre is

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$(0, 3)$

$(- 3, 0)$

$(0, - 3)$

$(3, 0)$

answer is D.

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Detailed Solution

$9 l^{2} + 6 l + 1 = 5 (l^{2} + m^{2})$
$\Rightarrow | \frac{3 l + 1}{\sqrt{l^{2} + m^{2}}} | = \sqrt{5} \Rightarrow c = (3, 0) .$

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