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Finding the locus

  1. Jun 23, 2013 #1
    1. The problem statement, all variables and given/known data
    Prove that the locus of middle points of all chords of the parabola ##y^2=4ax## which are drawn through the vertex is the parabola ##y^2=2ax##.


    2. Relevant equations



    3. The attempt at a solution
    The mid-point of the line joining the vertex and a point ##(h,2\sqrt{ah})## on parabola is ##(h/2,\sqrt{ah})## but what am I supposed to do with this? :confused:
     
  2. jcsd
  3. Jun 23, 2013 #2

    I like Serena

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    You have ##x=h/2## and ##y=\sqrt{ah}##. Eliminate h?
     
  4. Jun 23, 2013 #3
    Woops, I was trying this question from the last night and I couldn't even notice that. Very foolish of me. :redface:

    Thank you ILS! :smile:
     
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