(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the largest and shortest distance from origo to the ellipse.

2. Relevant equations

Ellipse: [itex]g(x, y) = 13x^2 + 13y^2 + 10xy = 72[/itex]

Function to optimize: [itex]F(x, y) = \sqrt{x^2 + y^2} [/itex]

But this is easier to optimize: [itex]f(x, y) = x^2 + y^2 [/itex]

3. The attempt at a solution

I set up the equations, [itex]\nabla f = \lambda \nabla g[/itex], which got me that [itex]x = y[/itex]. [itex]g(x) = 36x^2 = 72[/itex] and [itex]x^2 = 2[/itex] which got me that one of the values (either minimum or maximum) is [itex]F(x, y) = 2[/itex].

The question is, how do I get the other value?

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# Homework Help: Shortest & largest distance from origo to ellipse

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