P(2ap, ap^2) is a point on the parabola x^2 = 4ay. T is the foot of the perpendicular from P to the x-axis. R is the point where the tangent at P crosses the axis of the parabola. M is the midpoint of RT. Show that the locus of M is x^2 = -2ay

I'm having SO much trouble on this question, ive tried so many ways but they never come to that equation

I worked out that the co-ordinates of point R are (0,y) and T (2ap,0)

I then went and figured out the m(RT) and then the equation of RT.

m(RT) = -y/2ap

Then I worked out the midpoint of RT, M which was (ap, y/2)

but i am stuck on what to do next, i tried a few different approaches and they all didnt work, am i even going in the right direction?? T.T""

please helpp me !

thankyou =)