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Math Help - Vector calc center and radius of circle problem

  1. #1
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    Vector calc center and radius of circle problem

    I am studying for a test and one of the review questions is stumping me.

    I am suppose to find the center and radius of a circle with the following equation:

    x^2 + 4x + y^2 - 6y + z^2 + 12z = 0

    I know that the equation for a sphere is x^2 + y^2 + z^2 = radius ^2

    Also I think that you would take (x - x at center)^2 + (y- y at center)^2 + (z -- z at center)^2 and this is equal to the radius squared. But I do not know how to deal with 4x, -6y and 12z.
    Thanks to all you math enlightened folks for all the help that I have received for the past year!
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  2. #2
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    complete the square for x , y, and z ...

    x^2 + 4x + y^2 - 6y + z^2 + 12z = 0<br />

    (x^2 + 4x + 4) + (y^2 - 6y + 9) + (z^2 + 12z + 36) = 4 + 9 + 36

    can you finish?
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  3. #3
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    Vector calc center and radius answer response

    Thanks so much for your quick assistance.

    I see that by completing the squares we would have the square of the radius as 49 and therefore the radius is 7. I also see that the center coordinate would involve 2,3,6 but I think it would be (2, -3, 6) and the answer says it should be (-2,3, -6)????
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  4. #4
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    the book answer is correct

    (x - a)^2 + (y - b)^2 + (z - c)^2 = r^2<br />

    center at (a, b, c)
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