Results 1 to 7 of 7

Math Help - equation of a sphere

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    30

    Lightbulb equation of a sphere

    i have to show this equation represents a sphere..

    x^2 + y^2 + z^2 = 8x - 4y - 4

    but i'm stuck on the z variable as it won't come down to an even square. it comes down to a (x+2)(x-2).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by greencheeseca View Post
    i have to show this equation represents a sphere..

    x^2 + y^2 + z^2 = 8x - 4y - 4

    but i'm stuck on the z variable as it won't come down to an even square. it comes down to a (x+2)(x-2).
    Note that x^2 - 8x = (x - 4)^2 - 16 and y^2 + 4y = (y + 2)^2 - 4.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2010
    Posts
    30
    Quote Originally Posted by mr fantastic View Post
    Note that x^2 - 8x = (x - 4)^2 - 16 and y^2 + 4y = (y + 2)^2 - 4.
    ah, sorry i should have write (z+2)(z-2).. the other variables work out as even squares..
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Feb 2010
    Posts
    30
    so, what can i do about the z variable? i can't get it to work out as an even square..
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by greencheeseca View Post
    i have to show this equation represents a sphere..

    x^2 + y^2 + z^2 = 8x - 4y - 4

    but i'm stuck on the z variable as it won't come down to an even square. it comes down to a (x+2)(x-2).
    1. The general equation of a sphere with the center C(x_C, y_C, z_C) and the radius r is

    (x-x_C)^2+(y-y_C)^2+(z-z_C)^2=r^2

    2. Transform your equation until it has the form of the general equation:

    x^2 + y^2 + z^2 = 8x - 4y - 4

    Completing the square(s):

    x^2-8x + 16+y^2+4y+4 +z^2 = -4+16+4

    3. I'll leave the rest for you.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by greencheeseca View Post
    i have to show this equation represents a sphere..

    x^2 + y^2 + z^2 = 8x - 4y - 4

    but i'm stuck on the z variable as it won't come down to an even square. it comes down to a (x+2)(x-2).
    Quote Originally Posted by greencheeseca View Post
    so, what can i do about the z variable? i can't get it to work out as an even square..
    The only term with z in it is z^2 and I don't see what your problem could be with it. I have already shown you how to deal with the x-terms and y-terms.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,596
    Thanks
    1421
    Quote Originally Posted by greencheeseca View Post
    i have to show this equation represents a sphere..

    x^2 + y^2 + z^2 = 8x - 4y - 4

    but i'm stuck on the z variable as it won't come down to an even square. it comes down to a (x+2)(x-2).
    You apparently are trying to do this as
    (x^2- 8x)+ (y^2+ 4y)+ (z^2- 4)= 0
    which is wrong for two reasons. First, moving that "- 4" to the other side of the equation makes it " z^2+ 4" which cannot be factored, not " z^2- 4".

    But you don't want to do that to begin with!

    Instead leave that constant, 4, on the right and do it as (x^2- 8x)+ (y^2- 4y)+ (z^2)= -4

    Complete the square in x and y. The "z" term is already a perfect square! The numbers you need to add on the left to make the perfect squares, and, of course, add on the right, will give you a positive number on the right.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Sphere equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 23rd 2010, 09:07 PM
  2. Help - Equation of a sphere in 3D
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 11th 2010, 07:26 AM
  3. Find the equation of a sphere
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 6th 2009, 04:44 AM
  4. Find Equation of Sphere
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: October 13th 2008, 06:31 AM
  5. find the equation of the sphere
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 27th 2007, 02:57 PM

Search Tags


/mathhelpforum @mathhelpforum