1. (i) (Grade 11) $a, b, c$ are real numbers, and the sets are
$$
\begin{array}{l}
A=\left\{x \mid x=a^{2}-4 a\right\}, \\
B=\left\{y \mid y=b^{2}+2 b-3\right\}, \\
C=\left\{z \mid z=\sqrt{c^{2}+6 c+10}-5\right\}
\end{array}
$$

The relationship between them is ( ).
(A) $A=B=C$
(B) $A \cap B \cap C=\varnothing$
(C) $A \cup B \cup C=\mathbf{R}$
(D) None of the above
(ii) (Grade 12) If the ellipse $\frac{x^{2}}{2 a^{2}}+\frac{y^{2}}{b^{2}}=1$ and the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{2 b^{2}}=1(a, b>0)$ have the same foci, then the eccentricity of the ellipse is $(\quad)$.
(A) $\frac{\sqrt{3}}{2}$
(B) $\frac{\sqrt{15}}{3}$
(C) $\frac{\sqrt{6}}{4}$
(D) $\frac{\sqrt{30}}{6}$
(i) A.
$$
A=B=C=\{t \mid t \geqslant-4\} \text {. }
$$
(ii) D.

From $2 a^{2}-b^{2}=a^{2}+2 b^{2}$, we get $a^{2}=3 b^{2}$.
$$
e^{2}=\frac{2 a^{2}-b^{2}}{2 a^{2}}=\frac{5 b^{2}}{6 b^{2}}=\frac{5}{6}, e=\frac{\sqrt{30}}{6} .
$$