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.