Five, find the length of the chord intercepted by the graph $x^{2}+y^{2}-2 a x \cos \alpha-2 b y \sin \alpha$ $-a^{2} \sin ^{2} \alpha=0$ on the $y$-axis.
Let $\mathbf{x}=0$, the equation of the circle becomes
$$
\mathrm{y}^{2}-2 \mathrm{by} \sin \alpha-\mathrm{a}^{2} \sin ^{2} \alpha=0 \text {. }
$$

By Vieta's formulas, we have
$$
\begin{aligned}
y_{1} & +y_{2}=2 b \sin \alpha, y_{1} y_{2}=-a^{2} \sin ^{2} \alpha, \\
\text { chord length } & =\left|y_{1}-y_{2}\right|=\sqrt{\left(y_{1}+y_{2}\right)^{2}-4 y_{1} y_{2}} \\
& =\sqrt{4 b^{2} \sin ^{2} \alpha+4 a^{2} \sin ^{2} \alpha} \\
& =2|\sin \alpha| \sqrt{a^{2}+b^{2}} .
\end{aligned}
$$