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Math Help - Complete the square to find center and radius of the sphere

  1. #1
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    Complete the square to find center and radius of the sphere

    I have an odd problem in my book that i am trying to solve but dont have the solution to.
    Can anyone help me?

    Find the center and radius of the sphere whose equation is:

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

    Attempt:

    (x^2 + 2x + 1) -1 (y^2 - y - 1/4) + 1/4 + z^2 = 0
    (x^2+1)^2 + ( y^2 - 1/2)^2 + z^2 = 1 - 1/4 = 3/4

    r =  r^2 = 3/4
    r=  \sqrt {3/4}

    radius: 2 \sqrt {3}

    Center: (-1, + 1/2, 0)

    Am i correct?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Complete the square to find center and radius of the sphere

    You are not correct with:

    r=\sqrt{\frac{3}{4}}

    but even if you were, this simplifies to:

    r=\frac{\sqrt{3}}{2}
    Last edited by MarkFL; May 1st 2013 at 12:56 PM. Reason: haste makes waste
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  3. #3
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    Re: Complete the square to find center and radius of the sphere

    Quote Originally Posted by icelated View Post
    I have an odd problem in my book that i am trying to solve but dont have the solution to.
    Can anyone help me?

    Find the center and radius of the sphere whose equation is:

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

    Attempt:

    (x^2 + 2x + 1) -1 (y^2 - y - 1/4) + 1/4 + z^2 = 0
    Yes, x^2+ 2x+1= (x+ 1)^2 is a perfect square. However, -1(y^2- y- 1/4) is NOT. And, of course, you don't want " y^2" inside the square. What you want is y^2- y+ 1/4- 1/4. The constant term on such a square is always positive. That is, you want (x+ 1)^2+ (y- 1/2)^2+ z^2= 5/4.

    (x^2+1)^2 + ( y^2 - 1/2)^2 + z^2 = 1 - 1/4 = 3/4

    r =  r^2 = 3/4
    r=  \sqrt {3/4}

    radius: 2 \sqrt {3}

    Center: (-1, + 1/2, 0)

    Am i correct?
    Last edited by HallsofIvy; May 1st 2013 at 12:50 PM.
    Thanks from MarkFL and icelated
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  4. #4
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    Re: Complete the square to find center and radius of the sphere

    hello
    Attached Thumbnails Attached Thumbnails Complete the square to find center and radius of the sphere-444444444.jpg  
    Thanks from icelated
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  5. #5
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    Re: Complete the square to find center and radius of the sphere

    Thank you so much.
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