Parametrics Question (1 Viewer)

[frog0101]

Hi,
I am unable to prove this question out of the Cambridge textbook, any help would be great:
P is a variable point on the parabola x^2=4y. The normal at P meets the parabola again at Q. The tangents at P and Q meet at T. S is the focus and QS=2PS.
Prove that angle (PSQ)=90 degrees
Thanks heaps

 

[jazz519]

One way it can be done is by finding the coordinates for Q in terms of p by letting the normal at P be x + py=p^3+ 2p (a = one since the parabola isn't in x^2=4ay) and substitute x^2/4=y. Find the x and y coordinates for Q through that. Then through Pythagoras prove PQ^2=QS^2+PS^2, which shows the angle is 90 degrees