1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Homework Helper
    Gold Member

    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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook