# Converting from Parametric to Implicit

• Oct 4th 2008, 10:08 AM
butterfly
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! :)
• Oct 4th 2008, 10:55 PM
earboth
Quote:

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:

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

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

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

$\displaystyle \frac14 x^2 - \frac12 xy - \frac12 x + \frac14y^2 - \frac12y +1=0$
• Oct 6th 2008, 02:26 AM
lufbrastudent13
any chance butterfly is from loughborough? lol