Consider the parabola represented by the parametric equations $x=t^2-2t+2;y=t^2+2t+2$. Then which of the following is/are true?

$x=t^2-2t+2;y=t^2+2t+2$

$x+y=2(t^2+2)$ and $y-x=4t$

$\frac{x+y}{2}=\frac{{(y-x)}^2}{16}+2\Rightarrow {(y-x)}^2=8(x+y-4)$

${\left(\frac{y-x}{\sqrt{2}}\right)}^2=4\sqrt{2}\left(\frac{x+y-4}{\sqrt{2}}\right)$

This is parabola for which $y=x$ is axis,  $x+y=4$  is tangent at vertex and length of latus rectum is $4\sqrt{2}$