We substitute $x=1$ into the equation $xy^2-y-2=0$ to get $y^2-y-2=0$. This is a quadratic equation in $y$ which can be factored as $(y-2)(y+1)=0$. So, the solutions are $y=2$ and $y=-1$. Therefore, the points on the curve where $x=1$ are $(1,2)$ and $(1,-1)$.
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