Answer :
[tex]x^2+y^2+4x-6y+12=0 \\
y^2-6y+9=-x^2-4x-3\\
(y-3)^2=-x^2-4x-3\\
y-3=\sqrt{-x^2-4x-3} \vee y-3=-\sqrt{-x^2-4x-3}\\
y=3+\sqrt{-x^2-4x-3} \vee y=3-\sqrt{-x^2-4x-3}[/tex]
[tex]x^2+y^2+4x-6y+12=0\\\\x^2+2x\cdot2+2^2+y^2-2y\cdot3+3^2-2^2-3^2+12=0\\\\(x+2)^2+(y-3)^2-4-9+12=0\\\\(x+2)^2+(y-3)^2-1=0\\\\(y-3)^2=1-(x+2)^2\\\\(y-3)^2=[1-(x+2)][1+(x+2)]\\\\(y-3)^2=(-x-1)(x+3)\\\\y-3=\sqrt{-(x+1)(x+3)}\\\\y=3+\sqrt{-(x+1)(x+3)}[/tex]
