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. $\frac{35}{2\sqrt{34}}$

Answer 1

The correct option is C

$\frac{35}{3\sqrt{34}}$

The given lines can be written as

$5x+3y-7=0...\left(1\right)$

$5x+3y+\frac{14}{3}...\left(2\right)$

Let d be the distance between the lines $5x+3y-7=0$ and $15x+9y+14=0$

Then, $d=\left|\frac{-7-\frac{14}{3}}{\sqrt{5^2+3^2}}\right|$

$\Rightarrow d=\frac{35}{3\sqrt{34}}$