The general equation of a conic is as follows

ax² + 2hxy + by² + 2gx + 2fy + c = 0 where a, b, c, f, g, h are constants

For a circle, a = b and h = 0.

The equation becomes:

x² + y² + 2gx + 2fy + c = 0…(i)

Given, x² + y² + x - y = 0

Comparing with (i) we see that the equation represents a circle with 2g = 1 , 2f = - 1 and c = 0.

Centre ( - g, - f) =

= ().

Radius =