A problem about vectors and surfaces

[oahsen]

Homework Statement

Find the set of all points on the surface (y + z)^2 + (z − x)^2 = 16 where the
normal line is parallel to the yz-plane. Describe this set.

The Attempt at a Solution

I find the gradient vector of the surface then I said that the f at f*i should be zero when it is parallel to yz plane. then I found z=x for all x and z.Is my answer true and what is the desxription of this set is it the plane of z=x?

Thanks

 

[HallsofIvy]

Yes, that is exactly right.