Finding Intersection of Parametric Equation and Axis

Hi, I've been trying to learn the C4 paper ahead of schedule and have gotten down to one last question I can't quite get.

Q5) A curve C has parametric equations , . Show that the equation of the normal to C at the point P, whose parameter is , is:

The normal to C at P meets the x-axis at Q. The perpendicular from P to the x-axis meets the x-axis at R. Find the length of QR.

This is my working so far:

(Chain Rule)

Normal Gradient =

=

(Use p as parameter for normal equation)

(As required)

And thats about as far as I got, I've been trying to let y = 0 and let q be the parameter, so:

But do you then make them equal to each other and figure it out from there? I don't really know, its a WJEC paper too so I can't get any marking schemes without paying, so I thought this way would be better to get an understanding.

Thanks