Distance between the lines 5x + 3y – 7 = 0 and 15x + 9y + 14 = 0 isA

1.	Distance between the lines 5x + 3y – 7 = 0 and 15x + 9y + 14 = 0 isA. \(\frac{35}{\sqrt{34}}\) D. \(\frac{1}{3\sqrt{34}}\) C. \(\frac{35}{3\sqrt{34}}\) D. \(\frac{35}{2\sqrt{34}}\)
Answer» 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 Then, d = \(\Big\|\frac{(-7-\frac{14}{2})}{\sqrt{5^2+3^2}}\Big\|\) ⇒ d = \(\frac{35}{3\sqrt{34}}\)

Distance between the lines 5x + 3y – 7 = 0 and 15x + 9y + 14 = 0 isA. \(\frac{35}{\sqrt{34}}\) D. \(\frac{1}{3\sqrt{34}}\) C. \(\frac{35}{3\sqrt{34}}\) D. \(\frac{35}{2\sqrt{34}}\)

Answer»

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

Then, d = \(\Big|\frac{(-7-\frac{14}{2})}{\sqrt{5^2+3^2}}\Big|\)

⇒ d = \(\frac{35}{3\sqrt{34}}\)