A) 3 : 4
B) 1 : 2
C) 2 : 3
D) 4 : 1
Correct Answer: D
Solution :
Let equation of line thourgh 0(0, 0) is\[\frac{x}{\cos \theta }=\frac{y}{\sin \theta }=r\]If this line meets \[3y=10-4x\] at A then \[3r,\,\sin \theta =10-4\,{{r}_{1}},\cos \theta \] \[{{r}_{1}}\,(3\sin \theta +4\cos \theta )=10\] ??...(i) Again the line meets \[8x+6y+5=0\]at B \[\Rightarrow \,\,\,8{{r}_{2}}\cos \theta +6{{r}_{2}}\sin \theta +5=0\] \[\Rightarrow \,\,2{{r}_{2}}(3\sin \theta +4\cos \theta )=-5\] ??...(ii) by\[\frac{1}{2}\] \[\Rightarrow \]\[\frac{{{r}_{1}}}{2{{r}_{2}}}=\frac{10}{-5}\] \[\Rightarrow \] \[\frac{{{r}_{1}}}{{{r}_{2}}}=-\frac{4}{1}=4\]
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