3. If point $P\left(x_{0}, y_{0}\right)$ is such that the chord of contact of the ellipse $E: \frac{x}{4}+y^{2}=1$ and the hyperbola $H: x^{2}-\frac{y^{2}}{4}=1$ are perpendicular to each other, then $\frac{y_{0}}{x_{0}}=$ $\qquad$
3. $\pm 1$.

Point $P\left(x_{0}, y_{0}\right)$ has the tangent chord line equations for ellipse $E$ and hyperbola $H$ respectively as
$$
\frac{x x_{0}}{4}+y y_{0}=1, x x_{0}-\frac{y y_{0}}{4}=1 .
$$

From the fact that these two lines are perpendicular, we have
$$
\begin{array}{l}
\left(\frac{x_{0}}{4}, y_{0}\right) \cdot\left(x_{0},-\frac{y_{0}}{4}\right)=0 \\
\Rightarrow x_{0}^{2}-y_{0}^{2}=0 \Rightarrow \frac{y_{0}}{x_{0}}= \pm 1
\end{array}
$$