- #1
Inertigratus
- 128
- 0
Homework Statement
Find the largest and shortest distance from origo to the ellipse.
Homework 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]
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?