# Can you help convert the following parametric equ. to cartesian equ.

• Mar 16th 2012, 12:17 AM
vidhu
Can you help convert the following parametric equ. to cartesian equ.
$\displaystyle x=t(t-1)$
$\displaystyle y=4t/1-t$

Can you help me convert the above parametric equations to Cartesian equations by eliminating the "t" (Headbang) ?

thanks a lot (Rock)
Vidhu
• Mar 16th 2012, 12:28 AM
princeps
Re: Can you help convert the following parametric equ. to cartesian equ.
Quote:

Originally Posted by vidhu
$\displaystyle x=t(t-1)$
$\displaystyle y=4t/1-t$

Can you help me convert the above parametric equations to Cartesian equations by eliminating the "t" (Headbang) ?

thanks a lot (Rock)
Vidhu

$\displaystyle t^2-t-x=0 \Rightarrow t_{1,2}=\frac{1\pm \sqrt {1+4x}}{2}$
• Mar 16th 2012, 04:52 AM
Soroban
Re: Can you help convert the following parametric equ. to cartesian equ.
Hello, vidhu!

Quote:

$\displaystyle \begin{array}{ccc}x&=&\dfrac{t}{t-1} \\ y&=&\dfrac{4t}{1-t}\end{array}$

Can you help me convert the above parametric equations to Cartesian?

We have: .$\displaystyle \begin{Bmatrix}x &=& \dfrac{t}{t-1} & [1] \\ \\ y &=& \text{-}4\left(\dfrac{t}{t-1}\right) & [2] \end{Bmatrix}$

Substitute [1] into [2]: .$\displaystyle y \:=\:-4x$