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Quick parametric equation question

  1. Nov 19, 2009 #1
    1. The problem statement, all variables and given/known data


    Find a parametric representation for the lower half of the ellipsoid 3x^2 + 5y^2 + z^2 = 1
    x=u
    y=v

    z=??

    we need to find what z is


    3. The attempt at a solution

    i solved the equation for z getting

    z= sqrt(1-3x^2-5y^2)

    then i plugged the given x=u and y=v into equation
    to get
    z= sqrt(1-3u^2-5v^2)

    but that is wrong?
    what should i do instead??
     
  2. jcsd
  3. Nov 19, 2009 #2

    lanedance

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    Homework Helper

    shouldn't z be negtive for the lower half?
     
  4. Nov 19, 2009 #3
    :( yes... i need to learn how to read.
    thanks a lot lanedance
    that is right :)
     
  5. Nov 20, 2009 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Did the problem specifically say that you must use x and y themselves as parameters? There is enough "symmetry" here that I would have use "modified" spherical coordinates:
    [tex]x= \frac{\sqrt{3}}{3}cos(\theta)sin(\phi)[tex]
    [tex]y= \frac{\sqrt{5}}{5}sin(\theta)sin(\phi)[tex]
    [tex]z= cos(\phi)[/tex]
    with [itex]0\le \theta< 2\pi[/itex] and [itex]\pi/2 \le \phi \le \pi[/itex].
     
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