A straight line through origin ‘O’ meets the parallel lines $4 x + 2 y = 9$ and $2 x + y = - 6$ at point $P and Q$ respectively. Then the point ‘O’ divides the segment $P Q$ in the ratio

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$2 : 1$

$1 : 2$

$3 : 4$

$4 : 3$

answer is D.

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Detailed Solution

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Given parallel lines $4 x + 2 y = 9 \dots \dots \dots (1)$

$2 x + y = - 6 \dots \dots \dots (2)$

$O P : O Q =$ perpendicular distances from ‘O’ to line (1) and line (2)

$\begin{array}{l} = \frac{9}{\sqrt{16 + 4}} : \frac{6}{\sqrt{4 + 1}} \\ = \frac{9}{\sqrt{20}} : \frac{6}{\sqrt{5}} \\ = \frac{9}{2 \sqrt{5}} : \frac{6}{\sqrt{5}} \\ = \frac{3}{2} : 2 \\ = 3 : 4 \end{array}$

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