The correct option is B x2+y2−2x−2y+1=0
Given circle touching both the axes, then centre of circle is at (a,a).
and circle also touches 3x+4y=12
than diatance of (a,a) from 3s+4y=12 is equal to radius of circle.
radius of circle =|a|=(3a+4a−125)
|a|=∣∣∣7a−125∣∣∣
5a=7a−12 or −5a=7a−12
a=+1 or a=1
(x−1)2+(y−1)2=1
⇒x2+y2−2x−2y+1=0.