Find the maximum and minumum values of $\displaystyle s^2+t^2$ on the curve

$\displaystyle s^2+2t^2-2t=4$

by the method of Lagrange Multipliers.

If $\displaystyle s^2=4-2t^2+2t$ is substituted into $\displaystyle s^2+t^2$, we get a function

$\displaystyle h(t)=4+2t-t^2$

which has only a max value on R. Explain how the extreme values you obtained in the first part can be obtained from h(t).

I only know how to find the max and min from the orgin to to a surface, how do i deal with it when is from $\displaystyle s^2+t^2$