# Thread: Converting from Parametric to Implicit

1. ## Converting from Parametric to Implicit

Hi!

I was hoping that someone could give me a few guidelines as to how to find the Implicit representation of parametric equations, an example i need to solve has parametric equations,

x=t^2-t+t and y=t^2+t+1

I think i should have learnt this last year in my Vector Calculus module but we had problems with a very bad lecturer!

Thankyou for any replies!

2. Originally Posted by butterfly
Hi!

I was hoping that someone could give me a few guidelines as to how to find the Implicit representation of parametric equations, an example i need to solve has parametric equations,

x=t^2-t+t and y=t^2+t+1

I think i should have learnt this last year in my Vector Calculus module but we had problems with a very bad lecturer!

Thankyou for any replies!
1. Calculate t wrt x and y:

$\begin{array}{l}x=t^2-t+t \\ y=t^2+t+1\end{array}$ Subtract the second equation columnwise from the first on:

$x-y=-2t~\implies~t=-\frac12(x-y)$

2. Plug in this term for t either into the first or the second equation and you'll get:

$\frac14 x^2 - \frac12 xy - \frac12 x + \frac14y^2 - \frac12y +1=0$

3. any chance butterfly is from loughborough? lol