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# Choose the correct answer from the given four options. The distance between the lines $y = mx + c_1$ and $y = mx + c_2$ is

$\begin {array} {1 1} (A)\;\large\frac{c_1-c_2}{\sqrt{m^2+1}} & \quad (B)\;\large\frac{|c_1-c_2|}{\sqrt{1+m^2}} \\ (C)\;\large\frac{c_2-c_1}{\sqrt {1+m^2}} & \quad (D)\;0 \end {array}$

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A)
• Distance between parallel lines is $d = \bigg| \large\frac{c_1-c_2}{\sqrt{A^2+B^2}} \bigg|$
$y = mx+c_1$
$\Rightarrow mx-y+c_1=0$ $\therefore$ slope of this line is m and $y=mx+c_2$
$\Rightarrow mx-y+c_2=0 \therefore$ slope of this line is m.
$\therefore d = \bigg| \large\frac{c_1-c_2}{\sqrt{m^2+(-1)^2}} \bigg|$
$= \bigg| \large\frac{ c_1-c_2}{\sqrt{1+m^2}} \bigg|$