Paper 1, Section I, A

Variational Principles
Part IB, 2019

A function ϕ=xyyz\phi=x y-y z is defined on the surface x2+2y2+z2=1x^{2}+2 y^{2}+z^{2}=1. Find the location (x,y,z)(x, y, z) of every stationary point of this function.