Find the nature of the curve

Question

Given: $x=t^2+t+1, y=t^2-t+1$

Find the nature of the curve.

My approach: I was trying to relate $x$ and $y$. However I haven't been able to. Please suggest some methods to solve such kind of questions.

Answer 1

Would $x-y = 2t$ help you proceed? [Then you can plug $t = \frac{x-y}{2}$ back into one of the equations.]