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Math Help - Center and radius of circle.

  1. #1
    Junior Member
    Joined
    Sep 2009
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    Center and radius of circle.

    Alright so it says find the center and radius of THIS :

    x^2 + y^2 + x = 0

    Somehow they got numbers that WERENT variables in there

    (Moved the x's together and put them in brackets) Like this :

    (x^2 + x) + y^2

    (Then put these in)

    (x^2 + x + {1\over 4} - {1\over 4}) + y^2

    What the HELL did they do to be able to do that? Like it cancels out so can i put whatever numbers i want in there as long as they equal 0 or something? In that case wouldnt using 1 make it easier?

    Any explainations?

    Can post next steps of the answer if anyone would like
    Last edited by Djaevel; November 3rd 2009 at 10:28 AM. Reason: Messed up equation
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  2. #2
    MHF Contributor
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    It's called completing the square. You need to have the form of (x-h)^2+(y-k)^2=r^2 for a circle. When you have unfactored variables, you have to get it into a form that does factor.

    As long as the coefficient in front of the squared power (x^2 or y^2) is one, you take the coefficient in front of the x or y term, divide by 2 then square that. For your problem the coefficient was 1, divided by 2 is 1/2, and squared is 1/4. Since you added 1/4 you must also subtract it to keep equality. But now the x terms factor to (x+1/2)^2.

    It just takes practice. It's not a hard operation.
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