Problem involving chords at vertex of a standard parabola Chords AP and AQ are drawn through the vertex A of a parabola y² = 4ax 
 at right angles to one another. Prove that the line PQ cuts the axis in a fixed point. 
If I understand correctly, we're supposed to find the locus of the point on the axis and prove that it is constant. But I don't know how to start the deduction for the equation to PQ. 

Hint
Let $y=mx$ be the equation of AP
$$(mx)^2=4ax$$
$x=0, \dfrac{4a}{m^2}\implies P(4a/m^2,4a/m)$
Similarly $AQ: y=-\dfrac xm,Q:?$
Now find the equation of $PQ$ and it's intersection with $y=0$ the axis of the parabola
