Q2 of 38 Page 730

Show that the equation x2 + y2 + x – y = 0 represents a circle. Find its centre and radius.

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 =




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