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Math Help - Standard form & Graphing

  1. #1
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    Post Standard form & Graphing

    Good morning forum I need some assistance with the following question:

    Put the equation x2 + y2 + 8x + 2y = 29 into standard form and sketch the graph of the equation.

    Thanks AC
    Last edited by AlgebraicallyChallenged; January 25th 2009 at 05:33 AM. Reason: Didnt work previously
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  2. #2
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    Quote Originally Posted by AlgebraicallyChallenged View Post
    Good morning forum I need some assistance with the following question:

    Put the equation x2 + y2 + 8x + 2y = 29 into standard form and sketch the graph of the equation.

    Thanks AC
    I take it that the 2's are superscript.

    So it should read x^2 + y^2 + 8x + 2y = 29.

    First off, this is the equation of a circle.

    The standard form of a circle is (x - h)^2 + (y - k)^2 = r^2 where h is the x-coordinate of the centre, k is the y-coordinate of the centre, and r is the radius.

    To get it into this standard form, complete the square on the x terms and the y terms.

    x^2 + 8x + y^2 + 2y = 29

    x^2 + 8x + 4^2 + y^2 + 2y + 1^2 = 29 + 4^2 + 1^2

    (x + 4)^2 + (y + 1)^2 = 46

    [x - (-4)]^2 + [y - (-1)]^2 = (\sqrt{46})^2.


    So what's the centre? What's the radius? Can you sketch the circle?
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  3. #3
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    Quote Originally Posted by AlgebraicallyChallenged View Post
    Good morning forum I need some assistance with the following question:

    Put the equation x2 + y2 + 8x + 2y = 29 into standard form and sketch the graph of the equation.

    Thanks AC
    You have to complete squares, 8th grade trick.

    x^2+8x=(x+4)^2-16 and y^2+2y=(y+1)^2-1

    substituting this and rearranging the following is obtained:

    (x+2)^2+(y+1)^2=29+16+1=46

    this is a circle with center at (-2,-1) and radius \sqrt{46}
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  4. #4
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    Quote Originally Posted by andreas View Post
    You have to complete squares, 8th grade trick.

    x^2+8x=(x+4)^2-16 and y^2+2y=(y+1)^2-1

    substituting this and rearranging the following is obtained:

    (x+2)^2+(y+1)^2=29+16+1=46

    this is a circle with center at (-2,-1) and radius \sqrt{46}
    Wrong, it's a circle with centre at (-4, -1) and radius \sqrt{46}.
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  5. #5
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    Quote Originally Posted by Prove It View Post
    Wrong, it's a circle with centre at (-4, -1) and radius \sqrt{46}.
    Yes I admit, it was typo...
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