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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 PQ in the ratio.

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1 : 2

3 : 4

2 : 1

4 : 3

answer is B.

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Detailed Solution

Equation of the line through O parallel to the given lines is

$2 x + y = 0 . Let Q S T$ be perpendicular to these lines as in Fig.

$then \frac{O P}{O Q} = \frac{T S}{S Q}$

$\begin{array}{l} = \frac{distance between 2 x + y = 0 and 2 x + y = 9 / 2}{distance between 2 x + y = 0 and 2 x + y = - 6} \\ = \frac{9 / 2}{6} = \frac{3}{4} \end{array}$

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