Question

The distance between the parallel lines $5x-12y-14=0$ and $5x-12y+12=0$ is equal to :

• A. $\frac{1}{13}$
• B. $2$
• C. $\frac{2}{13}$
• D. $4$
• E. $\frac{4}{13}$

Answer 1

The correct option is B $2$

The distance between the parallel lines
$=\frac{|c_2-c_1|}{\sqrt{a^2+b^2}}$
Here, given lines are $5x-12y-14=0$ and $5x-12y+12=0$
Therefore, required distance, $d=\frac{|12-(-14)|}{\sqrt{5^2+(-12{)}^2}}$
$=\frac{12+14}{\sqrt{25+144}}=\frac{26}{\sqrt{169}}=\frac{26}{13}=2$