Normal and Parallel Lines

  1. Find an equation of each line normal to the graph y=2x/(x-1) and parallel to the line 2x-y+1=0
  2. jcsd
  3. HallsofIvy

    HallsofIvy 41,265
    Staff Emeritus
    Science Advisor


    Could you give us some indication as to what you DO understand about these problems and what you have already tried yourself?

    In particular, are these two separate problems or do you mean to find lines that are both normal to y= 2x/(x-1) AND parallel to 2x- y+ 1= 0?
  4. Pyrrhus

    Pyrrhus 2,204
    Homework Helper

    Use the concept of slope to solve this.
  5. I understand that a normal line is perpendicular and I know what the parallel line is. I know that you have to take a derivative to get the slope. But I'm assumimg the equation must be both normal and parallel(?)
  6. hmmm maybe by parallel they are refering to a tangent line???......well.......maybe lol :smile:
  7. HallsofIvy

    HallsofIvy 41,265
    Staff Emeritus
    Science Advisor

    Good! Now DO it! 2x-y+1= 0 is the same as y= 2x+ 1. What is the slope of that line? What is the slope of any line parallel to that?

    Find the derivative of y= 2x/(x-1) (as a function of x- you don't yet know what x is). Calling that m(x), the slope of the normal line is -1/m(x). Set that equal to the slope you got above and solve for x to find the point(s) at which the normal is parallel to 2x-y+1= 0.
  8. ehild

    ehild 12,942
    Homework Helper
    Gold Member
    2014 Award

    Is it meant as shown in the attachment?

    Last edited: Jun 29, 2010
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