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Q.
The distance $d$ between two parallel lines $y=m x+c_1 $ and $y=m x+c_2 $ is given by $d=\frac{z}{\sqrt{1+m^2}}$, where $z$ stands for
Straight Lines
Solution:
Two parallel lines can be taken in the form
and $ y =m x+c_1 ....$(i)
$y =m x+c_2....$(ii)
Line (i) will intersect $X$-axis at the point $A\left(-\frac{c_1}{m}, 0\right)$.
Distance between two lines is equal to the length of the perpendicular from point $A$ to line (ii). Therefore, distance between the lines (i) and (ii) is
$d=\frac{\left|(-m)\left(-\frac{c_1}{m}\right)+\left(-c_2\right)\right|}{\sqrt{1+m^2}} $
$d=\frac{\left|c_1-c_2\right|}{\sqrt{1+m^2}}$
Thus, the distanced between two parallel lines $y=m x+c_1$ and $y=m x+c_2$ is given by
$d=\frac{\left|c_1-c_2\right|}{\sqrt{1+m^2}} .$
