Question

The equation of the line passing through the point $(c,d)$ and parallel to the line $ax+by+c=0$, is

• A. $a(x+c)+b(y+d)=0$
• B. $a(x+c)-b(y+d)=0$
• C. $a(x-c)+b(y-d)=0$
• D. $a(x-c)-b(y-d)=0$

Answer 1

The correct option is C $a(x-c)+b(y-d)=0$

$ax+by+c=0$
So, the equation of the line which is parallel to the given line
$ax+by+\lambda =0$
It passes through $(c,d)$ is
$ac+bd+\lambda =0\Rightarrow \lambda =-(ac+bd)$
Now, the required equation of line
$ax+by-(ac+bd)=0\therefore a(x-c)+b(y-d)=0$