Alright im looking over some past exams in my calc 3 course, becaue i have a midterm, and one of the problems asks

Use Lagrange multipliers to find the rectangle of maximum perimeter wich has sides parallel to the coordinate axes and can be inscribed in the ellipse 3x^2+y^2=1.

I just need help with that problem and then this one aswell
Find the maximum and minimum value of f(x,y) = 2x^2+y^2 on the circle x^2+y^2=9.

i know the circle is a circle with radius 3.
and
partial f with respect to x is 4x
partial f with respect to y is 2y

how do i solve this then?