$26 \cdot 26$ The number of common points of the curves $x^{2}+4 y^{2}=1$ and $4 x^{2}+y^{2}=4$ is
(A)0.
(B) 1 .
(C) 2 .
(D) 3 .
(E) 4 .
(17th American High School Mathematics Examination, 1966)
[Solution] Standardizing the given curve equations, we have
$$
\begin{array}{l}
\frac{x^{2}}{1^{2}}+\frac{y^{2}}{\left(\frac{1}{2}\right)^{2}}=1, \\
\frac{x^{2}}{1^{2}}+\frac{y^{2}}{2^{2}}=1 .
\end{array}
$$

Both are ellipses, and the major axis of (1) is the minor axis of (2). Therefore, the common points of the two curves are only $(1,0)$ and $(-1,0)$ (the points of tangency of the curves).
Hence, the answer is $(C)$.