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. none of these

Answer 1

Answer: (C)

$a(x-c)+b(y-d)=0$

Equation of line parallel to $ax+by+c=0$ is $ax+by+k=0$ where k is constant.

As this line passes through $(c,d)$ then
$ac+bd+k=0\Rightarrow k=-ac-bd$

Therefore equation of line is
$a(x-c)+b(y-d)=0$