You are Here: Home >< Maths

# C4 parametric equations help

Announcements Posted on
TSR's new app is coming! Sign up here to try it first >> 17-10-2016
1. A curve has parametric equations: x = 2cos2t y = 6sint

a) find the gradient of the curve at the point where t = pi/3 (done this)

b) find a cartesian equation of the curve in the form:
y = f(x), -k < x < k

No idea what to do for b =S
2. Is there any way you can eliminate t from the equations, maybe using a trigonometric identity?
3. Tried using cos2t as 1 - 2sin^2t, but it didn't seem to work out.
4. As far as I'm aware that should work out...

What did you get for 2sin^2(t) then?
5. Erm... y = 6 - root(18x)
Can't find a mark scheme to check, but no idea where the K comes into it x_X
6. it should be y=3root(2-x)
x=2(1-2sin^2t) y=6sint
y^2=36sin^2t
(y^2)/36=sin^2t

x=2-4sin^2t
sub y
x=2-((Y^2)/9)

multiply through by 9

9x=18-(Y^2)
Y=root(18-9x)

thats what i get atleast

so -2<x<2
7. (Original post by nitinkf)
it should be y=3root(2-x)
x=2(1-2sin^2t) y=6sint
y^2=36sin^2t
(y^2)/36=sin^2t

x=2-4sin^2t
sub y
x=2-((Y^2)/9)

multiply through by 9

9x=18-(Y^2)
Y=root(18-9x)

thats what i get atleast

so -2<x<2
I concur.
8. Put x=2cos2t into the form x=2(2(cost)^2-1) or x=4(cost)^2-2

then y=6sint into Y^2=36(sint)^2

Then into identity (Sint)^2 + (cost)^2 = 1 in order to eliminate paramiter

The constant bit (K) is to show that you undersatnd the maximum and minimum x values of the cartesian equation.
9. Got it now, thanks all
10. For this one I got
$y=\frac{1}{2}\sqrt{2-x}$

EDIT: Just realised I forgot the 6! Dammit...
11. I've got the same question but can anyone help me with part a? I used the chain rule on it and and the whole dx/dt=1/(dt/dx) but I want to check my answer? :3
12. (Original post by revilowaldow)
I've got the same question but can anyone help me with part a? I used the chain rule on it and and the whole dx/dt=1/(dt/dx) but I want to check my answer? :3

I make it

If you get anything else and want someone to check it, then post your working.

## 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: July 19, 2012
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

### How does exam reform affect you?

From GCSE to A level, it's all changing

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