Question

How do you write the corresponding rectangular equation by eliminating the parameter `x = t^2 + t` and `y = t^2 - t`?

Answer 1

`x^2+y^2-2xy-2(x+y)=0`

Explanation:

Adding both equations we have `(x+y)/2= t^2` and subtracting then we obtain
`(x-y)/2=t` so the non-parametric equation is

`(x+y)/2=(x-y)^2/4` or

`x^2+y^2-2xy-2(x+y)=0` which is the equation of a parabola.