Find the equation of all lines having slope – 1 that are tangents to the curve y= 1 /(1-x) , x ≠ 1.
Find the equation of all lines having slope – 1 that are tangents to the curve y= 1 /(1-x) , x ≠ 1.

Given: Equation of the curve  ……….(i)

 

 = Slope of the tangent at 

But according to question, slope = 

  = 

 

 

  or 

From eq. (i), when 

And when  

  Points of contact are (2, 1) and 

And Equation of two tangents are  

 and

 =