A) 1 : 2
B) 2 : 1
C) 4 : 3
D) 3 : 4
Correct Answer: C
Solution :
Equation of line Perpendicular to \[2x+y+6=0\] passes through (0, 0) is \[x-2y=0\] Now point of intersection of \[x-2y=0\] and \[2x+y+6=0\]is \[\left( \frac{-12}{5},\frac{-6}{5} \right)\] and point of intersection of \[x-2y=0\] and \[4x+2y-9=0\] is \[\left( \frac{9}{5},\frac{9}{10} \right)\]. Now say origin divide the line \[x-2y=0\] in the ratio \[\lambda :1\] \ \[x=\frac{\frac{9}{5}\lambda -\frac{12}{5}}{\lambda +1}=0\Rightarrow \frac{9}{5}\lambda =\frac{12}{5}\], \[\therefore \lambda =\frac{4}{3}\] Thus origin divides the line \[x=2y\], in the ratio 4 : 3.
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