Question

Eliminate the parameter.

x = t2 + 2, y = t2 - 4

Answer 1

\(\bf x = t^2+2\qquad \qquad y = t^2-4\\ \quad \\ \quad \\
\textit{solving the 1st one for "t", we get}\\
x = t^2+2\implies \sqrt{x-2}= t\\ \quad \\
\textit{now that we know what "t" is, we substitute on the 2nd one}\\
y = t^2-4\implies y = \left(\sqrt{x-2}\right)^2-4\)

Answer 2

and if you expand the right-side, you'd get your rectangular equation