<span>As the paraboloids is given with the following equation
</span><span>x^2+y^2+ z=4 and x^2 +3y^2=z
So, </span><span>x^2+y^2+ z-4 = x^2 +3y^2 - z </span><span>x^2+y^2+ z-4 - x^2 -3y^2 + z =0 </span> = <span>-2y^2 +2z -4 </span>which is the projection of C onto the xy-Plane and it will be an eclipse.