Parallel and Perpendicular Lines - Practice Questions & MCQ

Line parallel and perpendicular to a given line

1. The equation of the line parallel to $a x+b y+c=0$ is given as $a x+b y+\lambda=0$, where $\lambda$ is some constant.

Equation of the given line is $a x+b y+c=0$
Its slope is $(-a / b)$
So, any equation of line parallel to $a x+b y+c=0$ is

$
\begin{aligned}
& y=\left(-\frac{a}{b}\right) x+c_1 \\
& a x+b y-b c_1=0 \\
& a x+b y+\lambda=0
\end{aligned}
$

2. The equation of the line perpendicular to $a x+b y+c=0$ is given as $b x-a y+\lambda=0$, where $\lambda$ is some constant.

Equation of the given line is $a x+b y+c=0$
Its slope is $(-a / b)$
Slope of perpendicular line will be (b/a)
So, any equation of line perpendicular to $a x+b y+c=0$ is

$
\begin{aligned}
& y=\left(\frac{b}{a}\right) x+c_1 \\
& b x-b y-a c_1=0 \\
& b x-a y+\lambda=0
\end{aligned}
$