Straight Line And Pair Of Straight Lines Ques 22
- A straight line through the origin $O$ meets the parallel lines $4 x+2 y=9$ and $2 x+y+6=0$ at points $P$ and $Q$ respectively. Then, the point $O$ divides the segment $P Q$ in the ratio
$(2000,1 M)$
(a) $1: 2$
(b) $3: 4$
(c) $2: 1$
(d) $4: 3$
Show Answer
Solution:
- Now, distance of origin from $4x + 2y - 9 = 0$ is
$$ \frac{|-9|}{\sqrt{4^{2}+2^{2}}}=\frac{9}{\sqrt{20}} $$
and distance of origin from $2x + y + 6 = 0$ is
$$ \frac{|6|}{\sqrt{2^{2}+1^{2}}}=\frac{6}{\sqrt{5}} $$
Hence, the required ratio $=\frac{9 / \sqrt{20}}{6 / \sqrt{5}}=\frac{3}{4}$
BETA
