Determine equations of all lines

[Kazane]

Homework Statement

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

Homework Equations

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??

 

[epenguin]

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.

 

[SammyS]

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

Then:
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.