Question

The distance between the parallel lines $3\cos \theta +4\sin \theta +\frac{5}{r}=0$ and $6\cos \theta +8\sin \theta +\frac{7}{r}=0$ is

• A. $\frac{3}{5}$
• B. $\frac{3}{10}$
• C. $\frac{3}{20}$
• D. $\frac{6}{5}$

Answer 1

Answer: (B)

$\frac{3}{10}$

Given equations of lines
$3\cos \theta +4\sin \theta +\frac{5}{r}=0$
or, $6\cos \theta +8\sin \theta +\frac{10}{r}=0$
$\Rightarrow 6r\cos \theta +8r\sin \theta +10=0$.....(i)
and $6\cos \theta +8\sin \theta +\frac{7}{r}=0$
$\Rightarrow 6r\cos \theta +8r\sin \theta +7=0$ .....(ii)
$d=\frac{|3|}{10}=\frac{3}{10}$