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Hyperbola point

  1. Mar 26, 2009 #1
    1) Find the point on the hyperbola xy=8 closest to (3,0).

    I honestly, have no idea what to do. I seriously do not remember discussing anything like this in class, nor having any previous problems in homework. If anyone can give me a start or walkthrough, that would be fantastic!
     
  2. jcsd
  3. Mar 26, 2009 #2
    Well, y = 8/x gives you a relation between the two variables that allows you to write the distance from (x,y) to (3,0) in terms of one variable, which can then be easily minimized.
     
  4. Mar 26, 2009 #3
    I've got D = 2rtx^2 - 6x + 9 + 64/x^2

    I'm not sure as to how this minimizes?
     
  5. Mar 27, 2009 #4

    HallsofIvy

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    HOW did you get that? What are r and t? What is D? There were not "r", "t", or "D" in your orginal statement of the problem.
     
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