[tex]x^2+y^2-6\sqrt{3}x+4\sqrt{5}y+47=0\\ \\ x^2-6\sqrt 3x+(3\sqrt 3)^2+y^2+4\sqrt 5 y+(2\sqrt 5)^2 = 0\\ \\ (x-3\sqrt 3)^2+(y+2\sqrt 5)^2 = 0 \\ \\ \Rightarrow x-3\sqrt 3 = 0\quad si\quad y+2\sqrt 5 = 0 \\\\ \Rightarrow \boxed{x = 3\sqrt 3}\quad si\quad \boxed{y = -2\sqrt 5}[/tex]
