p127 q8

Find the equation of the locus of the mid-point of a vairable chord thro' the point (a , 2a ) of the parabola $\displaystyle y^2=4ax$

thanks

edit: my working: let p be a point on $\displaystyle y^2=4ax$ , P = $\displaystyle (at^2 , 2at)$.

let A = (a, 2a)

equ of PA: $\displaystyle \frac {y-2a}{x-a} = \frac{2at-2a}{at^2-a}$

$\displaystyle y= \frac {2(x-a)}{t+1} +2a$

have no idea how to do