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Homework Help: Determine equations of all lines

  1. Jul 6, 2011 #1
    1. The problem statement, all variables and given/known data

    Determine equations of all lines the are tangent to y=x^2/(x-1) and that pass through the point (2,0).

    2. Relevant equations

    3. The attempt at a solution
    First I found the y' which I came up with y'=x(x-2)/(x-1)^2

    next, let (a,f(a)) and put a to y'
    f'(a)=a(a-2)/(a-1)^2 (slope of tangent lines at x=a) ->①
    also this slope is given by f(a)-0/a-2 -> ②
    ①=② then solve for a, but I stuck for calculating this...

    Am I on the right truck ?? can anyone help me, please??
  2. jcsd
  3. Jul 6, 2011 #2


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    You have the x,y co-ordinates of a general point on the curve, you have the slope of the tangent through that point, get the equation for that line. When you have done that I expect you can do the rest too.
  4. Jul 6, 2011 #3


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    What is the slope of a line passing through points (x1, y1) and (x2, y2) ?

    Let (x2, y2) = (a, f(a)), and (x1, y1) = (2, 0). You know the slope of the line passing through these two points must be f ' (a) , if the line is to be tangent to the curve y=x2/(x-1) at x = a.
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