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Parabola, tangebt line and Normal Line intersect

  1. Oct 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Where does the normal line to the parabola y= x - x^2 at the point (1,0) intersect the parabola a second time? Illustrate with a sketch

    2. Relevant equations

    y= x - x^2

    3. The attempt at a solution

    y' = 1-2x

    slope of tangent = -1 (after substituting value of x in above eq)

    -ve reciprocal of (-1) = 1

    equation of normal line is

    y - 0 = 1 (x -1)

    y = x -1

    After this I am not sure how to find the second point of intersection.

    I understand there has to be one since parabola is symmetric about its axis.

    Thank you.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 20, 2009 #2
    You've done everything correct so far. You now have a separate equation and you want to find where it intersects the parabola. By setting the equations equal, you will get your point of intersection.
     
  4. Oct 20, 2009 #3
    Thank you
     
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