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Let u = e^x and 1/u = 1/ e^x and just go about from there.

This. /End thread.

Thanks a lot everyone! makes a heck of a lot of sense now. I still need some work with parametrics though; although I highly doubt a question like that would be asked (yet).

I've also gotten what ohexploitable did, and they were the right answers. A little clueless as to how to attack the circle thing though. O_o

The tangent at P(2ap,ap^2) to the parabola x^2 = 4ay meets the x-axis at A. Find A. S is the focus of this parabola. Prove that SA is perpendicular to AP. Prove that the equation of the locus of the centre C of a circle through P,S, and A is the parabola x^2 = 2ay - a^2

Can I post up another question?

*sigh*, I knew it was something simple -.- Thanks anyways, sorry to bother you with a stupid question

It's not necessarily the difficulty of the question. I'm just confused as to why the a becomes a 1.

P(2p,p^2) is a variable point on the parabola x^2 = 4y, whose focus S and vertex O. M, N are the midpoints of SP, OM respectively. (i) Show the locus of M is the parabola y = 1/2(x^2 + 1), and find the locus of N. That isn't the full question. It's from Coroneos 3U btw. I don't know why I find...

In trying to do some locus problems, some of the questions which involve the focus (0, a) tend to switch the 'a' with a 1. I can't see how this works. I highly doubt my answer is wrong, but I'm pretty sure the answer in the back is also correct. It's probably a stupid question, but I would like...