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# FP3 Loci Help watch

1. 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 ^_^ .
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2. 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
3. (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
Well then why isn't my answer sufficient? Surely the coordinates I have stated show how the midpoint moves as t/a/b vary?
4. (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.
5. (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.
6. 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.
7. Bump
8. Bump
9. (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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