"x^2+y^2+z^2+2x+2y-z=2,"
"(x+1)^2-1+(y+1)^2-1+(z-\\frac12)^2-\\frac14=2,"
"(x+1)^2+(y+1)^2+(z-\\frac12)^2=4\\frac14."
The xy-plane intersects the sphere in a great circle, when coordinates of the centre are "(x_0, y_0, 0)."
We have "(-1, -1, \\frac12)."
The xy-plane does not intersect the sphere in a great circle.
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