Answer
$x^{2}-y^{2}=1, \quad x\geq 1,\qquad y\geq 0$
.
Work Step by Step
From the parametric equations, we find constrictions on x and y
$x\geq 1,\qquad y\geq 0$
Square both equations :$\left\{\begin{array}{l}
x^{2}=t+1\\
y^{2}=t
\end{array}\right.$
Substitute:
$x^{2}=y^{2}+1, \quad x\geq 1,\qquad y\geq 0$
$x^{2}-y^{2}=1, \quad x\geq 1,\qquad y\geq 0$
This is the upper right wing of a hyperbola.
To graph, create a function value table using values for t, in ascending order of t, calculating the x- and y-coordinates of points on the graph.
Plot and join the points obtained with a smooth curve, noting the direction in which t increases.
