The equation of a circle passing through ( 3, - 6) and touching both the axes, is 

Circles given in option $\left(a\right)$ passes through $( 3, - 6)$ and touches both the axes. 

ALITER The circle touching both the axes in the fourth quadrant is $x^2+y^2-2ax+2ay+a^2=0,a>0.$

It passes through (3,-6). 

$\therefore 45-6a-12a+a^2=0\Rightarrow a^2-18a+45=0\Rightarrow a=3,5$

So, the equations are 

$x^2+y^2-6x+6y+9=0$and $x^2+y^2-10x+10y+25=0$