1. 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. $3 y^{2}-x^{2}-16 y+20=0$
1. C Hint: According to the problem, we have $\frac{\sqrt{(x-4)^{2}+y^{2}}}{|x-3|}=2$, which simplifies to $3 x^{2}-y^{2}-16 x+20=0$.