Find the extreme value of function f(x,y) = x^2+2y^2 on the circle x^2+y^2 = 1?

Question

I know how to find the extreme value of a function but here the question says "on the circle" which really confused me. So can anyone help me here !?

Answer 1

extreme value means the maximum or minimum y value

which for a circle centered at the origin with radius = 1 is y=1 and y=-1

which are the absolute and relative max and mins or

(0,1) and (0,-1)