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Normal

The line lx+m...

Question

The line $l x + m y + n = 0$ is normal to the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0,$ if

l g + m f + n = 0

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l g + m f - n = 0

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l g - m f - n = 0

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l g - m f + n = 0

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Solution

The correct option is B $l g + m f - n = 0$
Given circle is
$x^{2} + y^{2} + 2 g x + 2 f y + c = 0$
Centre, $C = (- g, - f)$
Line $l x + m y + n = 0$ is normal to the given circle, so it passes through the centre,
$∴ - l g - m f + n = 0$
$\Rightarrow l g + m f - n = 0$

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