Question

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

Answer 1

Answer: (A)

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

Equation of line parallel to $ax+by+bc=0$ is $ab+by+d=0$

where $d$ is any constant

since this line passes through $\left(cd\right)$

so,

$a\times c+b\times d+d=0$

$=ac+bd+d=0$

$=d=-\left(ac+bd\right)$

therefore required equation of line is

$ax+by-\left(ac+bd\right)=0$

$ax+by-ac-bd=0$

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