Find the max/min values of s^2+t^2 on a curve by the method of Lagrange Multipliers

I've gotten an answer for the first half of this, but not the second one, which I believe is some sort of trick question.

Find the maximum and minimum values of on the curve

by the method of Lagrange Multipliers.

I already have this half answered, and got the following:

Max:

Min: ,

Now for the second half, which I believe is some sort of trick question.

If is substituted into , we get a function , which has only a maximum value on . Explain how the extreme values obtained in the first part can be obtained from .

See, the issue is that is a parabola, which has a maximum at 5, but no minimum (or at least no absolute minimum). So how would you use to find the minimum values? That's what I feel is the "trick" part of the question.

If anyone could clarify the second half of the question, I'd appreciate it.