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  4. The distance between the lines 5x - 12y + 65 = 0 and 5x - 12y - 39 = 0 is

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Q. The distance between the lines $5x - 12y + 65 = 0$ and $5x - 12y - 39 = 0$ is

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Solution:

The given lines are

$5x - 12y + 65 = 0 ...(i) $

and $5x - 12y - 39 = 0...(ii) $

Required distance $ = \left|\frac{65+39}{\sqrt{25+144}}\right|$

$\left(\because d = \frac{\left|c_{1}-c_{2}\right|}{\sqrt{a^{2}+b^{2}}}\right) $

$= \left|\frac{104}{13}\right| = 8 $ units