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Homework Help: Asymptote of curves problems

  1. Aug 17, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the set of values of m such that the asymtote of the curve,
    [tex]y=\frac{3(m+1)x+m-2}{(m-2)x+3m}[/tex] intersect at a point above the line y=3x-2

    2. Relevant equations



    3. The attempt at a solution

    Vertical asymtote, x=-3m/(m-2)

    horizontal asymtote, y=3(m+1)/(m-2)

    i am not sure how to move on.
     
  2. jcsd
  3. Aug 17, 2010 #2

    Mark44

    Staff: Mentor

    Re: asymtotes

    I believe this should say "such that the asymptotes of the curve..."
    The vertical and horizontal asymptotes intersect at (-3m/(m - 2), 3(m + 1)/(m - 2)). For this point to be above the corresponding point on the line y = 3x - 2, what are the conditions on m?
     
  4. Aug 17, 2010 #3
    Re: asymtotes

    I think all the intersections must lie on the line y=3x-1 but i am not sure what kind of conditinos to be imposed on m.
     
  5. Aug 17, 2010 #4

    Mark44

    Staff: Mentor

    Re: asymtotes

    No, it asks you to find the set of values of m such that the asymptotes of the curve...
    intersect at a point above the line y=3x-2.

    The two asymptotes intersect at (-3m/(m - 2), 3(m + 1)/(m - 2)). What are the coordinates of the line y = 3x - 2 when x = -3m/(m - 2)?

    What are the conditions on m so that the asymptote intersection is above the point on the line at which x = -3m/(m - 2)?
     
  6. Aug 18, 2010 #5
    Re: asymtotes

    ok, i will find y when x=-3m/(m-2)

    After this, do i calculate y>-3m/(m-2) for the ranges of m?
     
  7. Aug 18, 2010 #6

    Mark44

    Staff: Mentor

    Re: asymtotes

    Set up the inequality with the y value at the point of intersection (of the asymptotes) on one side, and the y value of the line on the other. For both points, use the same x value.
     
  8. Aug 18, 2010 #7
    Re: asymtotes

    ok thanks Mark.
     
  9. Aug 22, 2010 #8
    Re: asymtotes

    Is the answer m<14/52 and m>2 ?
     
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