Why is it obvious that the plane $z=0$ is tangent to the surface $z=x^{2}+y^{2}$ Why is it obvious that the plane $z=0$ is tangent to the surface $z=x^{2}+y^{2}$
I don't quite understand, is this obvious? I have a problem with the background knowledge, I don't even know how to deal with the surface $z=x^{2}+y^{2}$.

In fact at $z=0$ the equation $x^2+y^2=0$ defines only $1$ point, which is $(0,0)$.
So the plane $z=0$ and the surface intersect in a single point. 
But since the surface is smooth (the equation is polynomial), it cannot have singular points, and the touching point is automatically a tangent point.
