Question

The xy-plane intersects the sphere x^2+y^2+z^2+2x+2y-z=2 in a great circle.

Answer 1

The x-y-plane has standard equation z = 0.

$$x^2+y^2+0+2x+2y-0=2$$

$$(x+1)^2+(y+1)^2=4$$

The center of the great circle is $(-1,-1,0)$ and radius is $2.$