Finding the locus

1. Jun 23, 2013

Saitama

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?

2. Jun 23, 2013

I like Serena

You have $x=h/2$ and $y=\sqrt{ah}$. Eliminate h?

3. Jun 23, 2013

Saitama

Woops, I was trying this question from the last night and I couldn't even notice that. Very foolish of me.

Thank you ILS!