26-34 If the line $y=m x+1$ intersects the ellipse $x^{2}+4 y^{2}=1$ at one point (tangent), then the value of $m^{2}$ is
(A) $\frac{1}{2}$.
(B) $\frac{2}{3}$.
(C) $\frac{3}{4}$.
(D) $\frac{4}{5}$.
(E) $\frac{5}{6}$.
(22nd American High School Mathematics Examination, 1971)
[Solution] The two curves intersect at only one point, which means the quadratic equation $x^{2}+4(m x+1)^{2}=1$ has two equal roots, thus the discriminant is zero. That is, $\Delta=(8 m)^{2}-4\left(4 m^{2}+1\right) \cdot 3=0$, solving this gives $m^{2}=\frac{3}{4}$. Therefore, the answer is $(C)$.