You are Here: Home >< Maths

How do you find the cartesian equation of a curve? (C4)

Announcements Posted on
Four hours left to win £100 of Amazon vouchers!! Don't miss out! Take our short survey to enter 24-10-2016
1. Example question:
A curve is define by the parametric equations x=(t^2/2) + 1 and y=(4/t) -1
When t= 2, gradient is dy/dx = -1/2
Find a cartesian equation of the curve.

We havent learnt how to do it in school. I got this question from a past paper, and was just wondering how you'd do it.
Thanks!
2. (Original post by Phoebus Apollo)
Example question:
A curve is define by the parametric equations x=(t^2/2) + 1 and y=(4/t) -1
When t= 2, gradient is dy/dx = -1/2
Find a cartesian equation of the curve.

We havent learnt how to do it in school. I got this question from a past paper, and was just wondering how you'd do it.
Thanks!
Solve the easier equation for t and substitute into the other.
3. Or remove t from the simultaneous equations by other means eg. dividing.
4. (Original post by Phoebus Apollo)
Example question:
A curve is define by the parametric equations x=(t^2/2) + 1 and y=(4/t) -1
When t= 2, gradient is dy/dx = -1/2
Find a cartesian equation of the curve.

We havent learnt how to do it in school. I got this question from a past paper, and was just wondering how you'd do it.
Thanks!
It's kind of like solving simultaneous equations except trickier. Basically you want to see what you can do with and to eliminate , that'll get you in terms of or in terms of as required.

Here, you can kind of brute force it by doing

So .

But generally, you'll need to think about eliminating t and when you have trig parametric equations, you'll need to think about trigonometrical identities, etc...
5. For this type. Find t in terms of x and then substitute this expression of t into the equation for y. This eliminates t from the y equation leaving an equation in terms of x and y only - the Cartesian equation.
6. (Original post by Zacken)
...

Here, you can kind of brute force it by doing

So .

But generally, you'll need to think about eliminating t and when you have trig parametric equations, you'll need to think about trigonometrical identities, etc...
and you would complete with
.<<<< The 32 should be 8 but leaving it for the sake of history

Because you would never get a mark at C4 with .

Zacken knows this but you might not
7. (Original post by ODES_PDES)
Solve the easier equation for t and substitute into the other.
(Original post by morgan8002)
Or remove t from the simultaneous equations by other means eg. dividing.
(Original post by Zacken)
It's kind of like solving simultaneous equations except trickier. Basically you want to see what you can do with and to eliminate , that'll get you in terms of or in terms of as required.

Here, you can kind of brute force it by doing

So .

But generally, you'll need to think about eliminating t and when you have trig parametric equations, you'll need to think about trigonometrical identities, etc...
(Original post by B_9710)
For this type. Find t in terms of x and then substitute this expression of t into the equation for y. This eliminates t from the y equation leaving an equation in terms of x and y only - the Cartesian equation.
(Original post by nerak99)
and you would complete with
.

Because you would never get a mark at C4 with .

Zacken knows this but you might not
Thanks everyone
8. (Original post by nerak99)
and you would complete with
.
Surely it'd be ?
9. (Original post by Zacken)
Surely it'd be ?
Well I am nervous of arguing with you Zacken and you are correct

a) You kind of make my point and

b) You are right because I read it as a/(b/c) instead of (a/b)/c
10. (Original post by Zacken)
Surely it'd be ?
Brackets would help for clarity.
11. (Original post by Xenon17)
Brackets would help for clarity.
How would it?
12. (Original post by Zacken)
How would it?
. Could be written (which is unambiguous)

Although it still is a massive carbuncle.
13. (Original post by nerak99)
. Could be written
That's ruins the aesthetic and doesn't really help clear up any ambiguity since there is a visible and marked difference between

and
14. (Original post by Zacken)
That's ruins the aesthetic and doesn't really help clear up any ambiguity since there is a visible and marked difference between

and
Well There is no aesthetic in the double fraction form anyway but at least sticking brackets around the toip fraction makes it clear. If this were written by hand it would look like it could be a/b/c or a/b/c (ironic face) Hence the (a/b)/c we have here should be resolved to a/(bc) (smiley face, gritted teeth face, I am going for my tea now face)
15. (Original post by nerak99)
Well There is no aesthetic in the double fraction form anyway but at least sticking brackets around the toip fraction makes it clear. If this were written by hand it would look like it could be a/b/c or a/b/c (ironic face) Hence the (a/b)/c we have here should be resolved to a/(bc)
Ah, fair enough. I'll just simplify it down straight away next time, thanks.
16. Perhaps it would have helped if I hadn't £%@%\$&ed it up in the first place.

Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: April 27, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

Who is getting a uni offer this half term?

Find out which unis are hot off the mark here

Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read here first

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants