1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    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


    User Avatar
    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


    User Avatar
    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].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook