Question

Find the distance between the two parallel straight lines
$y=mx+c$ and $y=mx+d$.

Answer 1

Let $ax+by+c_1=0$ and $ax+by+c_2=0$ be two parallel straight lines then the distance between them is, $d=\left|\frac{c_2-c_1}{\sqrt{a^2+b^2}}\right|$

Therefore from given straight line the distance between those two lines is

$d=\left|\frac{c-d}{\sqrt{(-1{)}^2+m^2}}\right|$

$\Rightarrow d=\left|\frac{c-d}{\sqrt{1+m^2}}\right|$