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FP3 Loci Help

Okay, can someone explain to me what loci are? I have this question (attached below) and I have no idea what I'm really trying to get to. I got up to the midpoint of AB (a/2 cost, -b/2 cott). Now, now knowing what loci are, I stopped there, without knowing that there was more to it. So yeah, basically an indepth explanation on what they are and how they relate to my problem below would be amazing ^_^ .
(edited 13 years ago)
fp2locus.jpg44.5KB
Reply 1
Avatar for JamesyB
JamesyB
12
The locus is the set of co-ordinates that a point passes through as it is moved. So in this case as you move around the hyperbola, the midpoint of the line changes position so the locus is the set of points that the midpoint moves through. From there you need to get x and y in terms of t so that you can equate them to find the locus :smile:
Reply 2
Avatar for ViralRiver
ViralRiver
OP
16
Original post by JamesyB
The locus is the set of co-ordinates that a point passes through as it is moved. So in this case as you move around the hyperbola, the midpoint of the line changes position so the locus is the set of points that the midpoint moves through. From there you need to get x and y in terms of t so that you can equate them to find the locus :smile:


Well then why isn't my answer sufficient? Surely the coordinates I have stated show how the midpoint moves as t/a/b vary?
Reply 3
Avatar for anshul95
anshul95
11
Original post by ViralRiver
Well then why isn't my answer sufficient? Surely the coordinates I have stated show how the midpoint moves as t/a/b vary?

actually they usually specify a form you have to put it in to avoid people justing writing down the coordinates like that. But I don't know why but when someone says loci I wouldn't usually put the equations into parametric form. I suppose a habit really.
Reply 4
Avatar for JamesyB
JamesyB
12
Original post by anshul95
actually they usually specify a form you have to put it in to avoid people justing writing down the coordinates like that. But I don't know why but when someone says loci I wouldn't usually put the equations into parametric form. I suppose a habit really.


The equation for the locus should be just in terms of x and y, not t.
Reply 5
Avatar for ViralRiver
ViralRiver
OP
16
Hmm mixed opinions. Is there like a precise definition on what a locus actually is then? I've always thought it was a set of coords that mapped out the path of a point, which in my case is true. However, apparently it can't have parameters in it which just makes things confusing to be honest =\ - the book has no explanation so that doesn't help either.
Reply 6
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ViralRiver
OP
16
Bump
Reply 7
Avatar for ViralRiver
ViralRiver
OP
16
Bump
Original post by ViralRiver
Well then why isn't my answer sufficient? Surely the coordinates I have stated show how the midpoint moves as t/a/b vary?

your answer is right but in parametric form. you need to convert it to cartesian equation. thats why we find the value cost-sint/sect-tant (the one that is easier to find/applicable) in terms of x, a or y,a and convert it to cartesian using identities just like the way we learnt conversion of trigonometric parametric equation to cartesian equation in c4.
My homemade definition of locus- a point that moves with a certain rule ie follows a certain equation.

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