The condition for the line $l x + m y + n = 0$ to be a normal to the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ is

l g + m f = n

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l g + m f + n = 0

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l g + m f = 0

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l g = m f

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Solution

The correct option is A $l g + m f = n$
Every normal of circle passes through centre of circle.
$∴$ If $l x + m y + n = 0$ is normal to the circle
$x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ , then (-g,-f) lie on $l x + m y + n = 0$
$s o, l (- g) + m (- f) + n = 0$
$l g + m f - n = 0$

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