if the ordinates of the point on the parabola Y²=4ax axis twice the latus rectum prove that the abscissa of this point is twice the ordinate

We know that the latus rectum of a parabola  y² = 4ax  ...(1)  is given by 4a . Let the required point be (x , y) So by the given condition that ordinate of a point is twice the latus  rectum , we mean that
y = 2 x 4a = 8a.  ......(2)
This point satisfies (1) .
So we get (8a)² = 4ax where x is the abscissa of the point . 
we get 64a² = 4ax or 16a = x
x = 16 a = 2 x 8a = 2 x ordinate ( using (2) ).
Hence proved  . Hope that helps.