Show that the equation


Show that the equation $x^{2}+y^{2}+2 x+10 y+26=0$ represents a point circle. Also, find its centre. 



The general equation of a circle:

$x^{2}+y^{2}+2 g x+2 f y+c=0 \ldots$ (i) where $c, g, f$ are constants.

Given, $x^{2}+y^{2}+2 x+10 y+26=0$

Comparing with (i) we see that the equation represents a circle with $2 \mathrm{~g}=2 \Rightarrow \mathrm{g}=1,2 \mathrm{f}=$ $10 \Rightarrow f=5$ and $c=26$.

Centre $(-g,-f)=(-1,-5)$.

Radius $=\sqrt{g^{2}+f^{2}-c}$



Thus it is a point circle with radius 0.


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