Area of Parametric Equation

Since $t$ is a real number, $t^{2}$ will be always be non-negative. The minimum value of $y$ is $-1$ and the minimum value of $x$ is $-2$ .

We can subtract the given equations to get $y- x = 1$ . It's graph looks like this

It is not a complete line since $x$ cannot be less than $-2$ and $y$ cannot be less than $-1$ . It is, in fact, a ray starting at the point (-2, -1).

Its intercepts are $(-1,0 )$ and $(0,1)$ . These two points along with the origin form a right triangle. The lengths of the legs of the right triangle are both 1. Therefore the area of the triangle is $\frac{1}{2} \times 1 \times 1 = \boxed{0.5}$ $_\square$