This assignment is my Everest.Quote:

http://img75.imageshack.us/img75/615/circstt8.png

Explain why the minimum value of x^2+y^2 on x+y=4 occurs at the point at which a graph of x^2+y^2=Constant is tangent to the line x+y=4

Then

Using this answer, and implicit differentiation to find the slope of the circle, find the minimum value of x^2+y^2 such that x+y=4.