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Math Help - Need help finding (h,K,) and the radius of a circle

  1. #1
    Member M670's Avatar
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    Need help finding (h,K,) and the radius of a circle

    so my equation is x2+y2-4x+2y-4=0
    i know the formula is (x-h)2+(y-k)2=r2

    x2-4x+y2+2y-4=0

    the Y is (y-2)2 which makes my k equal to positive 2 just having trouble with the h and radius
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  2. #2
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    Re: Need help finding (h,K,) and the radius of a circle

    x^2+y^2-4x+2y-4 = 0

    x^2 - 4x + y^2 + 2y = 4

    complete the square for x and y ...

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

    finish it ...
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    Re: Need help finding (h,K,) and the radius of a circle

    Hello, M670!

    Sorry, your algebra is off . . .


    \text{Find the center and radius of the circle: }\:x^2+y^2-4x+2y-4\:=\:0

    We must "complete the square".

    \begin{array}{c}x^2 + y^2 - 4x + 2y - 4 \:=\:0 \\ \\ x^2 - 4x + y^2 + 2y \:=\:4 \\ \\ x^2 - 4x \,{\color{red}+\, 4} + y^2 + 2y {\color{blue}\,+\, 1} \:=\:4{\color{red}\,+\,4}{\color{blue}\,+\,1} \\ \\ (x-2)^2 +(y+1)^2 \:=\:9 \end{array}


    The circle has center (2,\text{-}1) and radius r = 3.
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  4. #4
    Member M670's Avatar
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    Re: Need help finding (h,K,) and the radius of a circle

    ok I understand that question but given this example here 5 x^2 - 10 x +5 y^2 - 8 y - 6 = 0 .

    I worked it down to (x-1)^2 and (y-0.8)^2 =
    I divided out 5 and was left with x^2-2x+y^2-1.6y-1.2=0
    then its x^2-2x+1 + y^2-1.6y ?= 1.2-1 (?)
    Last edited by M670; October 20th 2012 at 09:44 AM.
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    Re: Need help finding (h,K,) and the radius of a circle

    Quote Originally Posted by M670 View Post
    ok I understand that question but given this example here 5 x^2 - 10 x +5 y^2 - 8 y - 6 = 0 .

    I worked it down to (x-1)^2 and (y-0.8)^2 =
    I divided out 5 and was left with x^2-2x+y^2-1.6y-1.2=0
    then its x^2-2x+1 + y^2-1.6y ?= 1.2-1 (?)
    Why do you have 1.2-1 (?)?
    It clearly should be 1.2+(1)+(.64)
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    Member M670's Avatar
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    Re: Need help finding (h,K,) and the radius of a circle

    Quote Originally Posted by Plato View Post
    Why do you have 1.2-1 (?)?
    It clearly should be 1.2+(1)+(.64)
    The ? was because I was unsure if it would be .64 or something esle
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  7. #7
    Member M670's Avatar
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    Re: Need help finding (h,K,) and the radius of a circle

    How do you figure it out when you have a fraction or decimal to complete the squares?
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    Re: Need help finding (h,K,) and the radius of a circle

    Quote Originally Posted by M670 View Post
    How do you figure it out when you have a fraction or decimal to complete the squares?
    It is one-half the coefficient of the 'middle term' squared.
    \left(\frac{-1.6}{2}\right)^2=0.64.
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