Question 975231
{{{x^2-4x+y^2-6y=3}}} in form {{{(x-a)^2+(y-b)^2=r^2}}}

{{{(x^2-4x)+(y^2-6y)=3}}}......complete squares

{{{(x^2-4x+b^2)-b^2+(y^2-6y+b^2)-b^2=3}}}

{{{(x^2-4x+2^2)-2^2+(y^2-6y+3^2)-3^2=3}}}

{{{(x-2)^2-4+(y-3)^2-9=3}}}

{{{(x-2)^2+(y-3)^2-13=3}}}

{{{(x-2)^2+(y-3)^2=3+13}}}

{{{(x-2)^2+(y-3)^2=16}}}

{{{(x-2)^2+(y-3)^2=4^2}}}

so, {{{h=2}}}, {{{k=3}}}, and {{{r=4}}}

the center is at ({{{2}}},{{{3}}})


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(2,3,.12), locate(2,3,C(2,3)),
 graph( 600, 600, -10, 10, -10, 10,-sqrt(16-(x-2)^2)+3, sqrt(16-(x-2)^2)+3)) }}}