so plug that into the cone equation to get so
so and now complete the square and add to both sides so
and this is an ellipse which can be parameterized with sin and cos similar to how you would parameterize a circle
"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.