How to find the intersection of a cylinder and a plane?

[seto6]

Homework Statement

The plane x+y+z=1 cuts the cylinder x^{2}+y^{2}=1 in an ellipse. Find the points on this ellipse that lie closests to and farthest from the origin.

Homework Equations

N/A

The Attempt at a Solution

first step was to determine the intersection of the plane and the cylinder.
so x+y+z=x^{2}+y^{2}, but i am kinda stuck solving this
i got to this far but i am really stuck, (x-3)(x+2)+6+(y-3)(y+2)+6=z.
any hints will really be appriciated, since this is one of the past exam questions. if i can find the intersection i can go on from there.

 

[lanedance]

do you know lagrange multipliers?

just minimise distance to origin, or similarly x^2 + y^2 + z^2, with the constraints being the plane and the cylinder

 

[seto6]

thank you very much Lanedance,
i can not believe that i did not think of Lagrange multipliers.