Answer
See graph
Work Step by Step
$$x^2+y^2+2x+12y-12=0$$
$$x^2+2x+y^2+12y=12$$
Complete the square twice.
$$x^2+2x+1+y^2+12y+36=12+1+36$$
$$(x+1)^2+(y+6)^2=49$$
This is a circle with center (-1,-6) and a radius of 7 units.
Points are:
$$(-8,-6)$$
$$(6,-6)$$
$$(-1,1)$$
$$(-1,-13)$$
Plot these points and connect with a smooth circle.
