I'm doing my Math level $2$ SAT subject test and there is a problem in the book that says "The resulting equation of eliminating $t$ may consist of points not on the graph of the original set of equations" So, can you explain this for me with maybe an example please?
They also have this question : In the graph of the parametric equations : $x = t^2 +t , y = t^2 -t $,
A) $x\geq 0$
B) $x>= -1/4$
C) $x\in\mathbb{R}$
D) $x\geq -1$
E) $x\leq 1$
Note : It is allowed to use a graphing Calculator .
The answer written in the book to be B . But I still don't understand how, and even if I wanted to use my Calculator, how do I predict which value to give $T$ min, so that it would show me that the least value of $x$ is $-1/4$. Thanks Tons :) I really appreciate it .
For the first question: $$x=t^2+1,y=t^2+2\\ y-x=1$$ The point $(0,1)$ is on the second curve but not the first.