A circle which touches the positive axes, and whose centre it at distance 2√ from the origin, then the equation is
x 2+y2 - 4x-4y+4=0
Let O and C be the origin nad the centre of the circle respectively.
C = (r,r)
OC = 2√⇒OC2 = 8
C = (2,2,) r = 2 ⇒2r2 = 8⇒r2 = 4⇒r = 2
(x−2)2+(y−2)2 = 22⇒x2+y2−4x−4y+4 = 0