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Show that the equation x2 + y2 + 2x + 10y + 26 = 0 represents a point circle. Also, find its centre.

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The general equation of a circle: 

x2 + y2 + 2gx + 2fy + c = 0…(i) where c, g, f are constants.

Given, x2 + y2 + 2x + 10y + 26 = 0 

Comparing with (i) we see that the equation represents a circle with 2g = 2

⇒g = 1, 2f = 10

⇒f = 5 and c = 26. 

Centre ( - g, - f) = ( - 1, - 5). 

Radius = \(\sqrt{g^2+f^2-c}\) 

\(\sqrt{1^2+5^2-26}\) 

\(\sqrt{26-26}\) = 0.

Thus it is a point circle with radius 0

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