Question 1051880
<pre><b>
{{{3x^2+3y^2+6x-5y+2}}}{{{""=""}}}{{{0}}}

{{{3x^2+6x+3y^2-5y}}}{{{""=""}}}{{{-2}}}

{{{x^2+2x+y^2-expr(5/3)y}}}{{{""=""}}}{{{-2/3}}}

{{{(x^2+2x)+(y^2-expr(5/3)y)}}}{{{""=""}}}{{{-2/3}}}

Complete the square in the first parentheses by
adding {{{(expr(1/2)*2)^2=1) to both sides.

Complete the square in the first parentheses by
adding {{{(expr(1/2)*expr(5/3))^2=(5/6)^2=25/36) to both sides.

{{{(x^2+2x+1)+(y^2-expr(5/3)y+25/18)}}}{{{""=""}}}{{{-2+1+25/36}}}

{{{(x+1)^2+(y-5/6)^2}}}{{{""=""}}}{{{37/36}}}

Compare to

{{{(x-h)^2+(y-k)^2}}}{{{""=""}}}{{{r^2}}}

{{{-h="" + 1}}}, {{{-k=-5/6),  {{{r^2=37/36}}}
{{{h=-1}}}, {{{k=5/6}}}, {{{r=sqrt(37)/6}}}

center = (h,k) = {{{(matrix(1,3,-1,",",5/6))}}}
radius = r = {{{sqrt(37)/6}}}

Edwin</pre></b>