x Turn on thread page Beta
 You are Here: Home >< Maths

# FP3 Loci watch

1. I'm confused by what this term means. It's used in part b of the question attached, and while I follow the working, I have no idea what they did at the end to suddenly show what the locus of R is. If you can explain to me what a locus is in general, what it means here and how they got x=-a from pq=-1, I will be eternally grateful. I have a serious headache after looking at this stuff for the last few hours with no explanation in the book >< .
Attached Images

2. A locus is just a group of points satisfying a rule of some sort. Simple loci are often shapes or lines.

e.g. the locus of points 1 unit distance from (0,0) is the unit circle.
e.g. the locus of points that are equal distance from (-1,0) and (1,0) is the y axis (a straight line)

I can't see the question you attached so can't git more help I'm afraid.
3. (Original post by edavies)
A locus is just a group of points satisfying a rule of some sort. Simple loci are often shapes or lines.

e.g. the locus of points 1 unit distance from (0,0) is the unit circle.
e.g. the locus of points that are equal distance from (-1,0) and (1,0) is the y axis (a straight line)

I can't see the question you attached so can't git more help I'm afraid.
Thanks for that explanation, though it still doesn't solve my problem >< . I have now attached the problem to the first post.
4. (Original post by ViralRiver)
how they got x=-a from pq=-1, I will be eternally grateful.
Having arrived at pq = -1, we can now substitute into the position of the point R which is (apq,a(p+q)) to get (-a,a(p+q))

So the x co-ordinate of R is -a, i.e. fixed, and you have the line x= -a, or part of it.

IMHO, they need to show that the y co-ordinate of R, a(p+q) can take any value to show that the locus is the line, rather than just part of it.

a(p+q) can be written as a(p-1/p) since q=-1/p from your restriction pq=-1. And that can take any value, since as p goes to infinity so does a(p-1/p), and as p goes down to zero, a(p-1/p) goes to minus infinity, and it's continuous between the two, hence....

Turn on thread page Beta
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 22, 2011
Today on TSR

### How do I turn down a guy in a club?

What should I do?

Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
• create my feed
• edit my feed

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE