Question

The distance between the parallel lines $y=2x+4$ and $6x=3y+5$ is

• A. $\frac{17}{\sqrt{3}}$
• B. $1$
• C. $\frac{3}{\sqrt{5}}$
• D. $\frac{17\sqrt{5}}{15}$

Answer 1

Answer: (D)

$\frac{17\sqrt{5}}{15}$

Given equation of lines can be written as
$2x-y+4=0,2x-y-\frac{5}{3}=0$
Since, these lines are parallel .
So, $d=\frac{|c_1-c_2|}{\sqrt{a^2+b^2}}$
$\Rightarrow d=\frac{\frac{17}{3}}{\sqrt{5}}=\frac{17\sqrt{5}}{15}$