Some Improvements Needed

So for the hint I'd like to see a second hint explicitly writing down the multiplier step (ie including a discussion about the normal lines).

I'd also like to see a picture of the situation but that might be asking for a lot. I still find htat my visualization for these problems isn't great.

You mention in the hint and solution the sphere and the ellipse "just touch and do not intersect" which is a bit confusing. Things that touch do intersect even if just at a point right?

In the solution I would also like to see where the points came from (ie the explicitly plug in computation). I know its a second year course but we might as well be thorough.

Its a lot to ask for... sorry =)

Thanks, all has been done.