Question 1077350
{{{ x^2-10x+y^2+6y=15 }}} can be rewritten by completing the squares:
{{{ (x^2-10x + 25) + (y^2+6y + 9) = 15 + 9 + 25 }}}
{{{  (x-5)^2 + (y+3)^2 = 49 }}}

Compare this to the general form of the equation of a circle {{{ (x-x[0])^2 + (y-y[0])^2 = r^2 }}}
where ({{{ x[0] }}}, {{{y[0]}}}) = coordinates of the center

and you get
                
center at ( {{{ highlight(5) }}} ,{{{ highlight(-3) }}} )  and  {{{r = sqrt(49) = highlight(7))}}}