26・19 Let the moving point $M(x, y)$ be such that the ratio of its distance to the point $F(4,0)$ to its distance to the line $x=3$ is 2, then the equation of the locus of $M(x, y)$ is
(A) $\frac{x^{2}}{12}-\frac{y^{2}}{4}=1$.
(B) $\frac{x^{2}}{4}-\frac{y^{2}}{12}=1$.
(C) $3 x^{2}-y^{2}-16 x+20=0$.
(D) $3 y^{2}-x^{2}-16 y+20=0$.
(China Sichuan Province High School Mathematics Competition, 1989)
[Solution] According to the problem, we have $\frac{\sqrt{(\dot{x}-4)^{2}+y^{2}}}{|x-3|}=2$, which means
$$
3 x^{2}-y^{2}-16 x+20=0 \text {. }
$$

Therefore, the correct choice is $(C)$.