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Math Help - sketching a graph

  1. #1
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    sketching a graph

    how can i sketch x^2+y^2-16x+8y+16=0

    can you give me please try to explain the steps that i need to do


    thanks
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  2. #2
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    Quote Originally Posted by Candy101 View Post
    how can i sketch x^2+y^2-16x+8y+16=0

    can you give me please try to explain the steps that i need to do


    thanks
    it's a circle ... complete the square for both x and y and get it into the form

    (x-h)^2 + (y-k)^2 = r^2

    (h,k) is the center ... r is the radius
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  3. #3
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    Quote Originally Posted by Candy101 View Post
    how can i sketch x^2+y^2-16x+8y+16=0

    can you give me please try to explain the steps that i need to do


    thanks
    this is a circle that needs to be put in standard form to easily sketch it. I was able to realize that since the coefficients of the x^2 and y^2 are the same, namely =1

    We must complete the square for both x and y, so we divide the coefficient of the x and y terms by 2, square them, and add them to both sides

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

    And now we can factor

    (x-8)^2+(y+4)^2=64+16-16=64

    Can you sketch that now or do you need further assistance?
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  4. #4
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    i dont really know how to sketch it...
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  5. #5
    Senior Member pacman's Avatar
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    (x - 8)^2 + (y + 4)^2 = 64 = 8^2

    compare it with the standard equation of a circle, that is

    (x - h)^2 + (y + 4)^2 = r^2,

    h,k is the CORDINATE of the center of the CIRCLE, where r is the radius.

    from (x - 8)^2 + (y + 4)^2 = 64 = 8^2; center coordinate is (h,k) is (8,-4) and r = 8.

    see the graph . . . .



    if the standard equation of the circle awe you, resort to point plotting, maybe you have not encounter yet ANALYTIC GEOMETRY.


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    Attached Thumbnails Attached Thumbnails sketching a graph-circle.gif  
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