FP2 Loci + C3 Differentiation

http://filestore.aqa.org.uk/subjects/AQA-MFP2-W-QP-JAN11.PDF Paper

http://filestore.aqa.org.uk/subjects/AQA-MFP2-W-MS-JAN11.PDF MS

Question 1(b) why does point P have to be on the real axis at (8,0)? Why can't it be a anywhere on the circle? As you could draw a horizontal half line at any point on its circumference.

Question 6(a) No matter how hard I try I cannot achieve the printed result. I differentiate it to (sect tant + sec^2t)/(sect + tant) -cost
I have tried manipulating it but I can't achieve the printed result. Any hints?

For 6)a) simplify the fraction.

Question 1(b) why does point P have to be on the real axis at (8,0)? Why can't it be a anywhere on the circle? As you could draw a horizontal half line at any point on its circumference.

You were given $\arg z_1 = 0$, so you need the point on the circle where this condition is satisfied.

Why can't I draw a half line that is horizontal (so argument is 0) at say point (4,2) which lies on the circle?

Not all horizontal lines have an argument of 0, where did you get that from?

Argument is only 0 on the real axis. Draw a line from the origin to the point (4,2). You can clearly see the argument isn't 0.

Oh right, I've become incredibly rusty on loci lol. If that's the case then why can't I put P on the origin?

$\arg (0)$ is indeterminate, because you can't exactly draw a line from the origin to the origin, as such.