Figure 2 Figure 2 shows a sketch of the parabola C with equation y²=
4ax, where a is a positive
constant. The point S is the focus of C and the point P(ap²,
2ap) lies on C where p > 0
(a) Write down the coordinates of S.
(1)
(b) Write down the length of SP in terms of a and p.
(1)
The point Q(aq², 2aq), where p≉q, also lies on C.
The point M is the midpoint of PQ.
Given that pq =-1
(c) prove that, as P varies, the locus of M has equation
y²= 2a(x – a)
(5)