1. ## x and y

$x=t^2+t$
$y=t^2-t$

How to find the relation between $x$ and $y$?

2. Hello, SengNee!

$\begin{array}{cccc}x&=&t^2+t & {\color{blue}[1]}\\ y&=&t^2-t & {\color{blue}[2]}\end{array}$

How to find the relation between $x$ and $y$?
Eliminate the parameter $t.$

Subtract [2] from [1]: . $x-y \:=\:2t\quad\Rightarrow\quad t \:=\:\frac{x-y}{2}$

Substitute into [1]: . $x \;=\;\left(\frac{x-y}{2}\right)^2 + \frac{x-y}{2}$

This simplifies to: . $x^2 - 2xy + y^2 - 2x - 2y \:=\:0$