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Find center and radii of a circule

  1. Jan 12, 2010 #1
    1. The problem statement, all variables and given/known data

    2x^2+2y^2+2z^2+x+y+Z=9
    find center and radii of the sphere

    2. Relevant equations

    moving like terms yeilds

    2x^2 + x + _ + 2y^2 + y + _ + 2z^2 + z + _ = 9

    3. The attempt at a solution

    divide out the 2 yeilds

    2[ x^2 + 1/2x + _ + y^2 + 1/2y + _ + z^2 + 1/2z + _ ] = 9/2

    complete the square

    1/2 / 2 = (1/4)^2 = 1/16

    adding term in

    x^2 + 1/2x + 1/16 + y^2 + 1/2y + 1/16 + z^2 + 1/2z + 1/16 = 9/2 + 3/16

    solving right side

    9/2 + 3/16 = 72/16 + 3/16 = 75/16

    factoring left side

    (x + 1/4)^2 + (y + 1/4)^2 + (z + 1/4)^2

    solving

    center = C{-1/4,-1/4,-1/4}
    radii = sqrt of 75/16 = (5 sqrt 3) / 4

    whoot!
     
  2. jcsd
  3. Jan 12, 2010 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Either drop the "2" at the start or the "2" in "9/2"- you can't have them both!

    Okay, now that leading "2" is gone.

    Looks good to me!
     
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