I'm a bit uncertain about how I solve this right; my calculations so far are
$9x^2+9y^2+27x+12y+19=0$
$(x^2+y^2+3x+(4/3)y+19/9=0$
$(x^2+(3/2)x+9/4) +(y^2+(2/3)y+4/9) =7/12$
I'm getting the right answer for circle of center points $(-3/2, -2/3),$ but I get ${\sqrt 7/12}$ instead of ${\sqrt 21/6}$; what am I missing? Many thanks!
$$\sqrt{7/12}=\dfrac{\sqrt{7/3}}2=\dfrac{\sqrt{21}}6$$