Question

Distance between the lines 5x + 3y − 7 = 0 and 15x + 9y + 14 = 0 is
(a) $\frac{35}{\sqrt{34}}$

(b) $\frac{1}{3\sqrt{34}}$

(c) $\frac{35}{3\sqrt{34}}$

(d) $\frac{35}{2\sqrt{34}}$

(e) 35

Answer 1

(c) $\frac{35}{3\sqrt{34}}$

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

$$\begin{gathered} \mathrm{Then,}d=\left|\frac{-7-{\displaystyle \frac{14}{3}}}{\sqrt{5^2+3^2}}\right| \\ \Rightarrow d=\frac{35}{3\sqrt{34}} \end{gathered}$$