The equation of a circle with centre (h,k) and radius r is given as

(x-h)² + (y-k)²=r²

It is given that centre (h,k) =(1, 1) and radius (r) =.

Therefore, the equation of the circle is

(x-1)² + (y-1)²=

⇒ x² – 2x + 1 + y² -2y + 1 =2

⇒ ² + y² -2x -2y=0