Question

Find the distances between the following pair of parallel lines:

$3x+4y+9=0,6x+8y+15=0$

• A. $\frac{3}{10}$
• B. $\frac{3}{5}$
• C. $\frac{33}{10}$
• D. $\frac{24}{5}$

Answer 1

Answer: (A)

$\frac{3}{10}$

For lines $3x+4y+9=0$
And $6x+8y+15=0\Rightarrow 3x+4y+\frac{15}{2}=0$
Hence distance between them is

$\left|\frac{c_2-c_1}{\sqrt{{A_1}^2+{B_1}^2}}\right|$

$\left|\frac{\frac{15}{2}-9}{\sqrt{3^2+4^2}}\right|=\left|\frac{\frac{-3}{2}}{5}\right|=\frac{3}{10}$