http://www.physicsandmathstutor.com/download/Maths/A-level/FP3/Solutionbank-Heinemann/FP3%20Chapter%202.pdf#page=36Question and worked solution I'm stuck on in the link; I can't figure out how to do parts b and c.
My working:
a) as in worked solutions found that R (apq, a(p+q) )
b) gradient = 2/(p+q), insert (a, 0) into y=mx+c to get y(p+q) = 2x-2a ; which is equivalent to the equation found in the worked solutions when considering that pq=-1. Not sure how to get the locus of R being x=-a from that.
c) No working done as not sure how to find a locus as in b.
What I'm specifically stuck on:
- How to find the locus equation in b and c.
- Why inserting the coordinates of P into y=mx+c seems to work in the worked solutions, but inserting (a, 0), which the chord PQ passes through, doesn't.
- Most importantly: why finding the equation of the chord PQ has anything to do with finding the locus of R. R doesn't lie upon PQ, so what is the link? This is the part I need to understand most to be able to complete anything in this chapter.
Any help would be very much appreciated, I've been stuck on this for a couple of days and not been able to move on with the chapter, and exhausted every possible avenue to try to understand it. This is in the Edexcel FP3 book btw, Chapter 2 Ex F.