Answer
See graph
Work Step by Step
$$x^2+y^2+6x+10y-2=0$$
$$x^2+6x+y^2+10y=2$$
Complete the square twice.
$$x^2+6x+9+y^2+10y+25=2+9+25$$
$$(x+3)^2+(y+5)^2=36$$
This is a circle with center (-3,-5) and a radius of 6.
Points are:
$$(-9,-5)$$
$$(3,-5)$$
$$(-3,1)$$
$$(-3,-11)$$
Plot these points and connect with a smooth circle.
