6. Given the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)$ passes through the point $(2,1)$, then the set of all points on these ellipses that satisfy $|y|>1$ is represented by the shaded area in which of the following figures



保留了源文本的换行和格式，这是翻译结果。
Solve:
$\frac{4}{a^{2}}+\frac{1}{b^{2}}=1 \Rightarrow b^{2}=\frac{a^{2}}{a^{2}-4}5$, Substitute $b^{2}=\frac{a^{2}}{a^{2}-4}$ into $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ $\Rightarrow x^{2}+\left(a^{2}-4\right) y^{2}=a^{2} \Rightarrow a^{2}=\frac{4 y^{2}-x^{2}}{y^{2}-1}>5$, Combine with $|y|>1$ to get $x^{2}+y^{2}<5$.
Therefore, choose $C$.