The line $a x+b y+c=0$ is normal to the circle $x^2+y^2+2 g x+2 f y+d=0$ if

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Aicharya · Accepted Answer

Given, equation of circle is $ x^2+y^2+2 g x+2 f y+d=0 $ Its centre will be $(-g,-f)$. A normal to this circle will always passes through centre

Given, equation of line is $a x+b y+c=0$ If $a x+b y+c=0$, then it satisfied $(-g,-f)$ $ \begin{aligned} & \Rightarrow a(-g)+b(-f)+c & =0 \\ \Rightarrow & a g+b f-c & =0 \end{aligned} $

The line $a x+b y+c=0$ is normal to the circle $x^2+y^2+2 g x+2 f y+d=0$ if

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