Results 1 to 13 of 13

Math Help - graph an equation with x, y, z variables

  1. #1
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165

    Question graph an equation with x, y, z variables

    -x^2 - y^2 - 16z^2= 0

    how do i go about graphing this? all i know is it has to do with looking at "sections"
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    Err... unless x,y,z \in \mathbb{Z}, there is obviously only one solution to this: x=y=z=0 seeing as x^2, y^2, 16z^2 are all non-negative numbers...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    i know thats what i thought that's why i'm so confused i dont know how to graph it
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    Well, I suppose we would be looking at a single point in (0,0,0)...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    its just weird because they are supposed to be like spheres and paraboloids
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by holly123 View Post
    what is the general equation for an ellipsoid? i think -x^2-y^2-16z^6=0 might be an ellipsoid. trying to figure out how to graph it
    The general equation for an ellipsoid is \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}+\frac{(z-l)^2}{c^2}=1, where (h,k,l) is the center of the ellipsoid, and a>0,\,b>0,\,c>0.

    Unfortunately, the equation -x^2-y^2-16z^6=0 isn't an ellipsoid. I'm not even sure what to call it since the degree of z is 6... Are you sure you copied it down right?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    oh i'm sorry it's z^2!!
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by Chris L T521 View Post
    The general equation for an ellipsoid is \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}+\frac{(z-l)^2}{c^2}=1, where (h,k,l) is the center of the ellipsoid, and a>0,\,b>0,\,c>0.

    Unfortunately, the equation -x^2-y^2-16z^6=0 isn't an ellipsoid. I'm not even sure what to call it since the degree of z is 6... Are you sure you copied it down right?
    Quote Originally Posted by holly123 View Post
    oh i'm sorry it's z^2!!
    Ok, that's a little better. Are you sure its not -x^2-y^2{\color{red}+}16z^2=0? Because that would give us an elliptic [circular] cone!

    Note that -x^2-y^2+16z^2=0\implies z^2=\frac{x^2}{16}+\frac{y^2}{16}, which is an elliptic cone centered at (0,0,0).

    The graph would be as follows:
    Attached Thumbnails Attached Thumbnails graph an equation with x, y, z variables-mhf-quadricsurface.png  
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    i double checked and it's a subtraction sign
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by holly123 View Post
    i double checked and it's a subtraction sign
    That would cause some problems since -x^2-y^2-16z^2=0\implies z^2=-\frac{x^2}{16}-\frac{y^2}{16}\implies z=\pm\sqrt{-\frac{x^2}{16}-\frac{y^2}{16}}, which is imaginary since x^2>0 and y^2>0.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    i know i'm so stuck..any suggestions?
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by holly123 View Post
    i know i'm so stuck..any suggestions?
    I would suggust asking your professor about this. I believe there is a typo in the problem somewhere.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    okay thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 11th 2011, 02:29 AM
  2. Replies: 5
    Last Post: September 26th 2011, 07:37 AM
  3. Replies: 7
    Last Post: August 5th 2011, 01:30 PM
  4. Graph the linear equation with two variables?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 10th 2010, 07:41 PM
  5. Graph with three variables
    Posted in the Geometry Forum
    Replies: 6
    Last Post: May 8th 2009, 01:51 PM

Search Tags


/mathhelpforum @mathhelpforum