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