3. Given $P_{1}\left(x_{1}, y_{1}\right), P_{2}\left(x_{2}, y_{2}\right)$ are points on and outside the line $l$ respectively, if the equation of the line $l$ is $f(x, y)=$ 0, then the equation $f(x, y)-f\left(x_{1}, y_{1}\right)-f\left(x_{2}, y_{2}\right)=0$ represents
A. a line coinciding with $l$
B. a line passing through $P_{1}$ and perpendicular to $l$
C. a line passing through $P_{2}$ and parallel to $l$
D. a line not passing through $P_{2}$ but parallel to $l$
3. $\mathrm{C}$ Hint: Clearly $f\left(x_{1}, y_{1}\right)=0$, let the equation of $l$ be $A x+B y+C=0$, then $A x_{2}+B y_{2}+C \neq 0$, the equation $f(x, y)$ $-f\left(x_{1}, y_{1}\right)-f\left(x_{2}, y_{2}\right)=0$ is $A x+B y+C-A x_{2}-B y_{2}-C=0$.