4. Given $\odot O: x^{2}+y^{2}=5$ and the parabola $C$: $y^{2}=2 p x(p>0)$ intersect at point $A\left(x_{0}, 2\right), A B$ is the diameter of $\odot O$, and a line passing through point $B$ intersects the parabola $C$ at points $D$ and $E$. Then the product of the slopes of $A D$ and $A E$ is $\qquad$
4. 2 .

It is known that points $A(1,2), B(-1,-2)$. Let $D\left(x_{1}, y_{1}\right), E\left(x_{2}, y_{2}\right)$.
Since $B, D, E$ are collinear,
$$
\begin{array}{l}
\Rightarrow \frac{y_{1}+2}{x_{1}+1}=\frac{y_{2}+2}{x_{2}+1} \\
\Rightarrow y_{1} y_{2}+2\left(y_{1}+y_{2}\right)=4 \\
\Rightarrow k_{A D} k_{A E}=\frac{y_{1}-2}{x_{1}-1} \cdot \frac{y_{2}-2}{x_{2}-1} \\
=\frac{16}{y_{1} y_{2}+2\left(y_{1}+y_{2}\right)+4}=2 .
\end{array}
$$