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C4 parametric question

There are two questions I just can't do! The questions are : obtain a single Cartesian equation for each pair of parametric equations.. (1) X= t/t-1 and y = t/t+1. The second one is x= 2t/2t-3 and y = t/t+1
Original post by Remainresilient_
There are two questions I just can't do! The questions are : obtain a single Cartesian equation for each pair of parametric equations.. (1) X= t/t-1 and y = t/t+1. The second one is x= 2t/2t-3 and y = t/t+1


for 1) consider 1x,1y\frac{1}{x}, \frac{1}{y}

(and for 2, in fact)
(edited 8 years ago)
Reply 2
Avatar for B_9710
B_9710
18
You always want the same denominators on the fractions so that you add or substract them easily and hence find the Cartesian equation.
Or it is just possible to solve for t directly from the x-equation, then put it into the y-equation.
e.g. (1) x=t/(t-1) -> xt-x=t -> t(x-1)=x -> t=x/x-1. Thus y=(x/x-1)/((x/x-1)+1), then simplify.
Reply 4
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B_9710
18
Original post by constellarknight
Or it is just possible to solve for t directly from the x-equation, then put it into the y-equation.
e.g. (1) x=t/(t-1) -> xt-x=t -> t(x-1)=x -> t=x/x-1. Thus y=(x/x-1)/((x/x-1)+1), then simplify.


If you can find t in terms of x or y, then yes you can just substitute it into the other equation. Sometimes it may make the simplification a lot more difficult.
Reply 5
Avatar for TeeEm
TeeEm
19
Original post by constellarknight
Or it is just possible to solve for t directly from the x-equation, then put it into the y-equation.
e.g. (1) x=t/(t-1) -> xt-x=t -> t(x-1)=x -> t=x/x-1. Thus y=(x/x-1)/((x/x-1)+1), then simplify.


Original post by B_9710
If you can find t in terms of x or y, then yes you can just substitute it into the other equation. Sometimes it may make the simplification a lot more difficult.


I want to see a fight to the bitter end ....
Original post by TeeEm
I want to see a fight to the bitter end ....


In this case directly finding t is quite straightforward though.
Reply 7
Avatar for TeeEm
TeeEm
19
Original post by constellarknight
In this case directly finding t is quite straightforward though.


if he does not reply you won ....
Also see my reply to the other thread on graph transformations: an OCR MEI examiner's report says candidates must say "one-way stretch", not "squash" or "squeeze".

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