Straight Line and Pair of Straight Lines 1 Question 28
28. 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) $4: 3$
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Solution:
- Now, distance of origin from $4 x+2 y-9=0$ is
$$ \frac{|-9|}{\sqrt{4^{2}+2^{2}}}=\frac{9}{\sqrt{20}} $$
and distance of origin from $2 x+y+6=0$ is
$$ \frac{|6|}{\sqrt{2^{2}+1^{2}}}=\frac{6}{\sqrt{5}} $$
Hence, the required ratio $=\frac{9 / \sqrt{20}}{6 / \sqrt{5}}=\frac{3}{4}$
