1. “ $a=2, b=\sqrt{2}$ ” is the ( ) condition for “the curve $C: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ $(a 、 b \in \mathbf{R}, a b \neq 0)$ passes through the point $(\sqrt{2}, 1)$ ”.
(A) Sufficient but not necessary
(B) Necessary but not sufficient
(C) Sufficient and necessary
(D) Neither sufficient nor necessary
- 1. A.

The sufficiency is obviously true.
When the curve $C$ passes through the point $(\sqrt{2}, 1)$, we have $\frac{2}{a^{2}}+\frac{1}{b^{2}}=1$.
Clearly, $a=-2, b=-\sqrt{2}$ also satisfy the above equation. Therefore, the necessity does not hold.