Question

Give necessary calculations.Lazy answers will be deleted .

Answer 1

The point (3+3/√2,3/√2) doesn't satisfy the given equation of circle in option (1) and (3) .

hence the center of the circle given in the option 2 is (3/√2,3/√2)
and it is not lying on x-y = 3
hence option two can't be correct.
The center of the given circle in option 4 is (3,0)

and it lie on x-y = 3
then radius of this circle = √( 3+3/√2-3)²+(3/√2-0)² => √9/2+9/2 = 3