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# Parametric Equation watch

1. Attachment 730980

i) Was good, I got t = (1-x)/x
ii) Was good
iii) I found the y-coordinate as y = 1/(1-t)

question iv) The point Q is the intersection of the line x = 1/2 and the straight line joining the origin to the point T. Point R has co-ordinates (1/2, 0). Show that RQ = QP.

I am completely stuck on how to do this question.
Attached Images

2. (Original post by znx)

i) Was good, I got t = (1-x)/x
ii) Was good
iii) I found the y-coordinate as y = 1/(1-t)

question iv) The point Q is the intersection of the line x = 1/2 and the straight line joining the origin to the point T. Point R has co-ordinates (1/2, 0). Show that RQ = QP.

I am completely stuck on how to do this question.
Post a better quality image on https://imgur.com/ then post the link here.

The current image is impossible to read.
3. (Original post by RDKGames)
Post a better quality image on https://imgur.com/ then post the link here.

The current image is impossible to read.
Yeah sorry for that should be better now.
4. (Original post by znx)
Yeah sorry for that should be better now.
This question was asked before: https://www.thestudentroom.co.uk/sho...php?p=75995584
5. (Original post by RDKGames)
This question was asked before: https://www.thestudentroom.co.uk/sho...php?p=75995584
ah ok thank you
6. (Original post by RDKGames)
This question was asked before: https://www.thestudentroom.co.uk/sho...php?p=75995584
Thus, the gradient OT is given by , - I thought from ii) that the gradient m is found by dy/dx = -2t/(1-t)^2 ?
7. (Original post by znx)
Thus, the gradient OT is given by , - I thought from ii) that the gradient m is found by dy/dx = -2t/(1-t)^2 ?
Yeah that's the gradient along the curve.

OT is not along the curve.
8. (Original post by RDKGames)
Yeah that's the gradient along the curve.

OT is not along the curve.
I've still been struggling on the question, I used , and hence the line is
When x = 1/2 I plugged that into the parametric equation to find what t was at the point, however t cant be +/- 1. So I dont really know what to do tbh.
9. (Original post by znx)
I've still been struggling on the question, I used , and hence the line is
When x = 1/2 I plugged that into the parametric equation to find what t was at the point, however t cant be +/- 1. So I dont really know what to do tbh.
When , what is in terms of ?

Then you know the coordinates of the point Q in terms of . You also know the coords of R and P. So show that the distances RQ = QP
10. (Original post by RDKGames)
When , what is in terms of ?

Then you know the coordinates of the point Q in terms of . You also know the coords of R and P. So show that the distances RQ = QP
So i just sub x =1/2 into that equation for the line?
11. (Original post by znx)
So i just sub x =1/2 into that equation for the line?
Well, yeah.

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