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Use lagrange multipliers to find the shortest distance

  1. Feb 19, 2010 #1
    1. The problem statement, all variables and given/known data
    Use lagrange multipliers to find the shortest distance between a point on the elliptic paraboloid z=x^2 +y^2

    2. Relevant equations

    3. The attempt at a solution
    http://img716.imageshack.us/img716/7272/cci1902201000000.jpg [Broken]

    I'm not that good with using the equation editor, so I scanned my work.

    I'm stuck on the last part where i'm trying to factor the equation to find a solution for [tex]\lambda[/tex], I cant seem to find a solution that would make the equation zero, which is what i need in order to do the long division to factor that equation.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 19, 2010 #2


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    Your constraint is x^2+y^2-z=0. You differentiate lambda*(x^2+y^2-z). So you have a mistake on step 3. The d/dz equation should be 2*(z-1/2)=(-lambda). That may be why you are having a hard time with the resulting equation.
  4. Feb 19, 2010 #3
    ah, now the equation makes much more sense, thanks for the help.
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