"Let Σ denote that part of the cone x^2 + y^2 = z^2, z > 0 which lies beneath the plane x + 2z = 1.

Let F(x, y, z) = (0,x,0).

Show that the projection of ∂Σ vertically to the xy-plane is an ellipse. Parametrise ∂Σ."

I have no idea how they get an ellipse from this. I've substituted the plane equation into the cone equation and i get a set which isn't an ellipse and hence don't know how to parametrize this. I must be doing something wrong!

Any help would be greatly appreciated.

Thanks.