I have to find out the tangent planes to the graph of $f(x, y)=x^2+y^2$ that contain the intersection of the planes $x+y+z=3$ and $z=0$. I know that this intersection is the line $x+y=3$ and that if $(x_0, y_0, z_0)$ is the tangential point, the equation must be $$z-z_0=2x_0(x-x_0)+2y_0(y-y_0). $$ Please give me a hint about how to start
Update: the line $x+y=3$ is contained in $z=0$, so the intersection between $f$ and the plan $z=0$ is the origin. Hence that is a Tangent plan. Now I have to find out the other solution ($z=6x-6y-18$).