Join TSR now and get all your revision questions answeredSign up now

Lagrange multipliers question help please :) Watch

    • Thread Starter

    Find the rectangle in the ellipse  x^2 + 4y^2 = 1 with the smallest perimeter.

    I know that if  L = f(x,y) + \lambda g(x,y) then  \lambda g(x.y) = \lambda(x^2 + 4y^2 - 1) .

    However in the solutions it says that  f(x,y) = 4x + 4y . Why isnt this  2x+2y for the perimeter of the rectangle? Or is this a mistake in the solution? :/


    4x+4y is the perimeter of the rectangle.

    Think for a moment, the ellipse is one which is clearly centered at the origin.

    Hence, the length and breath of the rectangle would have to span both the -ve/+ve x and y axes in a symmetrical fashion to sit snugly within the ellipse.

    The horizontal side of the rectangle would be 2x.

    The vertical side of the rectangle would be 2y.

    Hence, perimeter would be 2* (2x+2y)= 4x+4y

    Hope this helps. Peace.
Would you shell out for travel insurance?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.