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Math Help - fixed point?

  1. #1
    Junior Member
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    fixed point?

    I don't know how to do

    HKCEE 1993 Paper I 10(c),

    even I read the solution already.



    C is the curve y = 1/(k+1) ( 2(x)^2 + (k + 7)x + 4 )

    Show that C always passes through two fixed points for all values of k not equal to -1. What are the coordinates of the two points?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ling_c_0202
    I don't know how to do

    HKCEE 1993 Paper I 10(c),

    even I read the solution already.



    C is the curve y = 1/(k+1) ( 2(x)^2 + (k + 7)x + 4 )

    Show that C always passes through two fixed points for all values of k not equal to -1. What are the coordinates of the two points?
    Take two cases of the family of curves C_1 and C_2 generated
    by letting k=1 and k=2 respectively.

    Then find the x-coordinates of the points of intersection of
    C_1 and C_2 (you should find these are -1 and -2).

    Now substitute these values of x back into the RHS of the equation of
    C and you will find that it is independent of k.

    So the points corresponding to the values of x that you have found are
    the same on all the curves (when k \neq -1).

    RonL
    Last edited by CaptainBlack; December 30th 2005 at 05:28 AM.
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  3. #3
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    thank you

    thank you very much!
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