we got the equation
$$r(t) = (t-2)i + (t^2+4)j$$
I got
$$x = 1-2t$$ $$y = 1+4t$$
Would that be correct?
2026-04-03 21:05:39.1775250339
Equation for the curve in terms of x,y
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If Your equation is a vector equation: $$ \vec r(t)= (t-2)\vec i +(t^2+4) \vec j $$ where $\vec i$,$\vec j$ are the versors of the orthogonal basis, than you have: $$ x=r_1=t-2 \qquad y=r_2=t^2+4 $$ So: $t=x+2$ and $y=(x+2)^2+4$.