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Math Help - Finding the center and radius of an equation

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    Finding the center and radius of an equation

    x^2 + y^2 - 2x - 8y = -1

    Can anyone thoroughly explain how to find the center and radius?
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  2. #2
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    Quote Originally Posted by emidavis View Post
    x^2 + y^2 - 2x - 8y = -1

    Can anyone thoroughly explain how to find the center and radius?
    You need to get it to the form

    [mth](x - h)^2+ (y - k)^2 = r^2[/tex].

    Then you can read off the centre as (h, k) and the radius as r.


    To do this in your case, you need to complete the square on x and y.


    x^2 + y^2 - 2x - 8y = -1

    x^2 - 2x + (-1)^2 + y^2 - 8y + (-4)^2 = -1 + (-1)^2 + (-4)^2

    (x - 1)^2 + (y - 4)^2 = 16

    (x - 1)^2 + (y - 4)^2 = 4^2.


    So the centre is (1, 4) and the radius is 4.
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