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

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 = 2g = 1, 2f = 10f = 5 and c = 26.


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


Radius =




Thus it is a point circle with radius 0.


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