Question

The distance between the lines $5x-12y+65=0$ and $10x-24y-39=0$ is

• A. $\frac{13}{5}$ units
• B. $\frac{169}{2}$ units
• C. $13$ units
• D. $\frac{13}{2}$ units

Answer 1

Answer: (D)

Given lines are $5x-12y+65=0$
and $10x-24y-39=0$
$\Rightarrow 5x-12y-\frac{39}{2}=0$
Since, given lines are parallel.
$\therefore$ Distance between the lines
$=\frac{|-\frac{39}{2}-65|}{\sqrt{5^2+{\left(-2\right)}^2}}=\frac{|-\frac{169}{2}|}{\sqrt{25+144}}$
$=\frac{\frac{169}{2}}{13}=\frac{13}{2}$ units