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Finding the distance between a point and a level curve

  1. Sep 14, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the point on the curve defined by 5/8 x^2 - 3/4 xy + 5/8 y^2 = 1

    That is closest to the point (1,-1)


    2. Relevant equations



    3. The attempt at a solution

    I started by finding the gradient vector. < (5/4x - 3/4 y) , (5/4y - 3/4x) >

    I could not figure out if that was even the right direction to go in because I don't know how I'd even find a distance formula
     
  2. jcsd
  3. Sep 14, 2009 #2

    tms

    User Avatar

    You have one equation with two unknowns, so you need another equation relating those two variables. You do have information to construct another equation: the distance from the curve to the specified point is a minimum. Write down an equation that expresses that condition, and then solve the two equations for the two unknowns.
     
  4. Sep 14, 2009 #3
    ah nvm i realized its just optimizing a function with another contraining function.. i think... so i could use lagrange multipliers

    thanks for your help
     
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