Find the equation of the tangent plane and the vectorial equation of the normal line of the surface

$$z = x^2 + y^2$$

at the point $(1,-2,5)$

For the vectorial equation of the normal line, should I consider the function $F(x,y,z) = x^2 + y^2 -z$ and $\vec{n} = \vec{\nabla}F(1,-2,5)$ as my normal vector?

I'm not sure of how should I do this.

Thanks!