Question

In the graph of the parametric equations $\{\begin{array}{c}x=t^2+t\\ y=t^2-t\end{array}$ for integral values of t.

• A. $x\ge 0$
• B. $x\ge -\frac{1}{4}$
• C. $x$ is any real number
• D. $x\ge -1$
• E. $x\le 1$

Answer 1

The correct option is A $x\ge 0$

$x=t^2+t=t(t+1)$

$x<0\forall t\in (-1,0)$

$\therefore x<0\Rightarrow t=$ not an integer.

$\therefore x⩾0$ for all integral values of $t$

A option is cvorrect.