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Find the distance between parallel lines 4x – 3y + 5 = 0 and 4x – 3y + 7 = 0

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Equations of the given parallel lines are 4x – 3y + 5 = 0 and 4x – 3y + 1 = 0 

Here, a = 4, b = – 3, c = 5 and c = 7

∴ Distance between the parallel lines

\(=\begin{vmatrix}\frac{c_1-c_2}{\sqrt{a^2+b^2}}\end{vmatrix}\)\(=\begin{vmatrix}\frac{5-7}{\sqrt{4^2+(-3)^2}}\end{vmatrix}\)

\(=\begin{vmatrix}\frac{-2}{\sqrt{16+9}}\end{vmatrix}\)\(=\begin{vmatrix}\frac{-2}{5}\end{vmatrix} = \frac {2}{5} units\)

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