Answer
The following is the sketch of the equation.
Work Step by Step
$x^2+y^2+6x-12y+45=0$
$x^2+6x+y^2-12y=-45$ (Add both with $9$ and $36$ to complete the square)
$x^2+6x+9+y^2-12y+36=-45+9+36$
$(x+3)^2+(y-6)^2=0$
The only point which satisfies the last equation is $(x,y)=(-3,6)$.
So, the graph of the equation is one point $(-3,6)$.
