4. Let the circle $O: x^{2}+y^{2}=5$ intersect the parabola $C: y^{2}=2 p x(p>0)$ at point $A\left(x_{0}, 2\right)$, and let $AB$ be the diameter of circle $O$. A line passing through $B$ intersects $C$ at two distinct points $D, E$. Then the product of the slopes of lines $AD$ and $AE$ is $\qquad$.
Answer: 2
Analysis: We can find the points $A(1,2), B(-1,-2)$, let $D\left(x_{1}, y_{1}\right), E\left(x_{2}, y_{2}\right)$, then from the collinearity of points $B, D, E$ we get
$$
\begin{array}{l}
\frac{y_{1}+2}{x_{1}+1}=\frac{y_{2}+2}{x_{2}+1} \Rightarrow y_{1} y_{2}+2\left(y_{1}+y_{2}\right)=4 \\
\Rightarrow k_{A D} \cdot k_{A E}=\frac{y_{1}-2}{x_{1}-1} \cdot \frac{y_{2}-2}{x_{2}-1}=\frac{16}{y_{1} y_{2}+2\left(y_{1}+y_{2}\right)+4}=2 .
\end{array}
$$