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!

Equation of ellipsoid and graph

  1. Sep 23, 2016 #1
    1. The problem statement, all variables and given/known data
    Equation of ellipsoid is:

    ##\frac{x^2}{4} + \frac{y^2}{9} + z^2 = 1##

    First part of the question, they asked to graph the equation. I have a question about this, I know that ##-1\leq z \leq 1##. So what happens when the constant 1 gets smaller after minusing some value of ##z^2##? Does it's "radius" get smaller?

    Second part of the question is:

    Is it posiible to find a function ##f(x,y)## so that this ellipsoid may be considered to be the graph of ##z=f(x,y)##?

    2. Relevant equations


    3. The attempt at a solution
    For the second part, I answered no, because the graph ##z=f(x,y)## is a function of the level curve of the graph of the ellipsoid.

    Am I right?

    Thanks.
     
  2. jcsd
  3. Sep 23, 2016 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    1 is 1, it cannot get smaller. What do you mean by "what happens", and what do you call radius?

    I don't understand your answer, but it does not contain the crucial point. If there would be such a function: What is e. g. f(0,0)? It needs a unique z-value.
     
  4. Sep 24, 2016 #3
    How do I graph this ellipsoid? I was trying to use the level curves method. By looking at the equation, I know that the value of ##z## cannot be more than 1. I was trying to set the value of ##z## to plot the graph. So I was trying to plot the level curves for ##x## and ##y##. That's why the value of 1 changes when I do this. Is what I'm doing wrong?

    I think I now get it. There's no such unique function for ##z=f(x,y)## because it is ##z^2## in the original equation. Hence there needs to be 2 functions, ##z = \pm \sqrt{[1 - \frac{x^2}{4} - \frac{y^2}{9}]}##.
     
  5. Sep 24, 2016 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    @toforfiltum: In response to your question of how to sketch an ellipsoid. Your example was$$
    \frac{x^2}{4}+ \frac{y^2} 9 + z^2 = 1$$ I'm going to assume that you know that if you have the equation$$
    \frac{x^2}{a^2}+ \frac{y^2} {b^2} = 1$$in the ##xy## plane, that gives an ellipse with ##x## intercepts ##(\pm a,0)## and ##y## intercepts ##(0,\pm b)##. You could lightly draw a rectangular box square with the axes through those four points and sketch a nice looking ellipse in that box.
    To sketch a 3D ellipsoid like the one you gave, you can just draw the traces in the coordinate planes. For example in the plane ##x=0## your equation would be ##\frac{y^2} 9 + \frac {z^2} 1 = 1##. Sketch that in the ##yz## plane with ##y## intercepts of ##\pm 3## and ##z## intercepts of ##\pm 1##. Do the other two traces similarly.
     
  6. Sep 24, 2016 #5

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    That is a possible approach. z cannot exceed 1 (and cannot be smaller than -1), sure, so you get curves for |z|<1. Add curves in the other planes for a nicer 3D illustration? Or use some predefined plotting algorithm that can draw the ellipsoid.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Equation of ellipsoid and graph
  1. Is this an ellipsoid? (Replies: 2)

  2. Graph of an equation (Replies: 4)

Loading...