The correct option is C (x+1)2+(y−6)2=2
|x+1|+|y−6|=2 is a square with centre (−1,6) which is centre of the circle also.
Distance between two parallel sides (x+1)+(y−6)=2 and (x+1)+(y−6)=−2
i.e., x+y=7 and x+y=3 is ∣∣∣−3+7√2∣∣∣=2√2
∴ Radius of required circle =√2
Hence, equation of the circle is (x+1)2+(y−6)2=2