13. Given point $A(0,2)$ and two points $B, C$ on the parabola $y^{2}=x+4$ such that $A B \perp B C$, find the range of the y-coordinate of point $C$.

 untranslated text remains unchanged.
13. 【Analysis and Solution】Let the coordinates of point $B$ be $\left(y_{1}^{2}-4, y_{1}\right)$, and the coordinates of point $C$ be $\left(y^{2}-4, y\right)$.

Clearly, $y_{1}^{2}-4 \neq 0$, so $k_{A B}=\left(y_{1}-2\right) /\left(y_{1}^{2}-4\right)=1 /\left(y_{1}+2\right)$. Since $A B \perp B C$, we have $k_{B C}=-\left(y_{1}+2\right)$. Therefore, $y-y_{1}=-\left(y_{1}+2\right)\left[x-\left(y_{1}^{2}-4\right)\right]$, and $y^{2}=x+4$. Eliminating $x$, and noting that $y \neq y_{1}$, we get: $\left(2+y_{1}\right)\left(y+y_{1}\right)+1=0 \rightarrow y_{1}^{2}+(2+y) y_{1}+(2 y+1)=0$. By $\Delta \geqslant 0$, we solve to get: $y \leqslant 0$ or $y \geqslant 4$.

When $y=0$, the coordinates of point $B$ are $(-3,-1)$; when $y=4$, the coordinates of point $B$ are $(5,-3)$, both satisfying the conditions. Therefore, the range of the y-coordinate of point $C$ is $y \leqslant 0$ or $y \geqslant 4$.