Hi guys

P and Q are the end points of a focal chord of the parabola $\displaystyle x^2 = 4ay $with focus S. If the coordinates of P and Q are(2ap,$\displaystyle ap^2$) and (2aq,$\displaystyle aq^2$) respectively.

(a) Write down the gradients of PS and QS.$\displaystyle \frac{p^2-1}{2p} $ and $\displaystyle \frac{q^2-1}{2q}$ respectively

(b) Show that pq = -1

(c) Find the coordinates of the midpoint R of PQ in terms of p. $\displaystyle [a(p-\frac{1}{p}), \frac{a}{2}(P^2+\frac{1}{p^2}]$

(d) Show that the equation of the locus of R is $\displaystyle x^2$ = 2a(y-a).

I've done what the question has asked me to do BUT my teacher wants me to go one step further and find the condition for the locus of R. Could someone please explain this to me - I dont geddit from the notes I've been given

Thanx a lot