Since the circle touches both the axis,let the radius of the circle by a,then

Case (i): If centre (a,a) but given centre lies on

$2a-a=3$

$a=3$

Centre =(3,3)

Radius =|3|=3

Equation of circle is $(x-3)^2+(y-3)^2=3^2$

Case (ii): If centre (-a,a) but given centre lies on

$2(-a)-a=3$

$-3a=3$

$a=-1$

Centre =(1,-1)

Radius =|-1|=1

Equation of circle is $(x-1)^2+(y+1)^2=1$

Case (iii): If centre (-a,-a) but given centre lies on

$2(-a)+a=3$

$-a=3$

$a=-3$

Radius =|-3|=3

Equation of circle is $(x-3)^2+(y-3)^2=3^2$

Case (iv): If centre (a,-a) but given centre lies on

$2x-y=3$

$2a+a=3$

$a=1$

Centre =(1,-1),radius =1

Equation of circle is $(x-1)^2+(y+1)^2=1$

Hence (a) is the correct answer.