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Help with Circle question, A level C2.

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    Hi all,

    I have been re-visiting old topics recently in prep. for the c2 exam. Today I am doing circles, but I can't do this question. I know I have done it before, but I have forgotten which makes it even more frustrating

    Show that the circle with equation x² + y² - 2ax - 2bx + b² = 0 touches the Y-axis.

    Thanks a lot for any help
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    At the y-axis you have x=0

    Set x=0 and see what happens
  3. Offline

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    (Original post by TenOfThem)
    At the y-axis you have x=0

    Set x=0 and see what happens
    Hi, I did that and got y² + b² = 0

    But how does this show that it touches the y axis?

    Thanks
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    I think that you have copied the question incorrectly and you should have -2by not -2bx
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    I don't think you can answer this question unless you have the values for a and b as they're the numbers that give you the translation from your original circle..
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    (Original post by TenOfThem)
    I think that you have copied the question incorrectly and you should have -2by not -2bx
    I double checked and the way I copied it is the way its in the book, but maybe this is a typo in the book? Out of interest, what would you do if it was -2by?
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    If it is -2by

    x^2 + y^2 - 2ax - 2by +b^2 = 0


    (x-a)^2 - a^2 + (y-b)^2 = 0

    (x-a)^2 + (y-b)^2 = a^2


    When x=0, y=b ... a single solution so the circle touches the y-axis at (0,b)



    So, yes, I think it is a typo in the book
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    (Original post by TenOfThem)
    If it is -2by

    x^2 + y^2 - 2ax - 2by +b^2 = 0


    (x-a)^2 - a^2 + (y-b)^2 = 0

    (x-a)^2 + (y-b)^2 = a^2


    When x=0, y=b ... a single solution so the circle touches the y-axis at (0,b)



    So, yes, I think it is a typo in the book
    Thats makes sense, thanks a lot!

    Stupid textbooks =_=

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