Currently stuck on my hw, to be handed in on Monday, wondering if anyone can help?

The normal to the parabola with the equation y^2=4ax at the point P(at^2, 2at) meets the curve again at the point Q (as^2, 2as). Show that s=-t-(2/t).

I'm not sure where the a, x and y have dissappeared to because when I worked out the equation to the normals at P and Q, I couldn't eliminate them.

Can someone shed any light on this please?