Finding the highest point on a curve of intersection of an ellipsoid and a plane

[sdobbers]

How would you go about finding the highest point on the curve of intersection of an ellipsoid and a plane? Given: x^2 + y^2 + z^2 = k and ax + by + cz = j. I was thinking about using Lagrange Multipliers but I would always get stuck.

 

[EnumaElish]

How did you set up the problem and where did you get stuck?