8. Given points $A(a-1, a), B(a, a+1)$, a moving point $P$ is such that its distance to point $M(1,0)$ is 1 unit greater than its distance to the $y$-axis, forming a curve $C$. If the line segment $AB$ intersects curve $C$ at exactly one point, then the range of values for $a$ is $\qquad$
8. $[-1,0] \cup[1,2]$
The trajectory equation of $C$ is $y^{2}=4 x$ and the ray $y=0(x \leqslant 0)$. $AB$ is equivalent to a line segment of length $\sqrt{2}$ on the line $y=x+1$. To ensure that $AB$ intersects with $C$, the range of $a$ must be controlled within $[-1,0] \cup[1,2]$.