Eliminate the parameter to find a Cartesian equation of the curve

Question

I've done every problem on this subject except I can't get this one. (every other problem had x = something and y = something.

$$y = (t+1)^{1/2},\quad y = (t-1)^{1/2}$$

Answer 1

$y=\sqrt{t+1},y=\sqrt{t-1}$ should be either of the followings :

If you mean $$x=\sqrt{t+1},\ \ y=\sqrt{t-1},$$ then we have $$x^2=t+1,y^2=t-1\Rightarrow x^2-y^2=(t+1)-(t-1)=2.$$

If you mean $$y=\sqrt{t+1},\ \ x=\sqrt{t-1},$$ then we have $$y^2=t+1,x^2=t-1\Rightarrow x^2-y^2=(t-1)-(t+1)=-2.$$