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Question
Distance between the lines 5x + 3y − 7 = 0 and 15x + 9y + 14 = 0 is
Options
\[\frac{35}{\sqrt{34}}\]
\[\frac{1}{3\sqrt{34}}\]
\[\frac{35}{3\sqrt{34}}\]
\[\frac{35}{2\sqrt{34}}\]
35
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Solution
\[\frac{35}{3\sqrt{34}}\]
The given lines can be written as
5x + 3y − 7 = 0 ... (1)
\[5x + 3y + \frac{14}{3} = 0\] ... (2)
Let d be the distance between the lines 5x + 3y − 7 = 0 and 15x + 9y + 14 = 0
\[\text { Then, d } = \left| \frac{- 7 - \frac{14}{3}}{\sqrt{5^2 + 3^2}} \right|\]
\[ \Rightarrow d = \frac{35}{3\sqrt{34}}\]
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