A) \[7:3\]
B) 3 : 7
C) \[2:3\]
D) None of these
Correct Answer: B
Solution :
Lines \[3x+4y+2=0\]and \[3x+4y+5=0\] are on the same side of the origin. The distance between these lines is \[{{d}_{1}}=\left| \frac{2-5}{\sqrt{{{3}^{2}}+{{4}^{2}}}} \right|=\frac{3}{5}\]. Lines \[3x+4y+2=0\] and \[3x+4y-5=0\]are on the opposite sides of the origin. The distance between these lines is \[{{d}_{2}}=\left| \frac{2+5}{\sqrt{{{3}^{2}}+{{4}^{2}}}} \right|=\frac{7}{5}\]. Thus \[3x+4y+2=0\] divides the distance between \[3x+4y+5=0\] and \[3x+4y-5=0\] in the ratio \[{{d}_{1}}:{{d}_{2}}\] i.e., \[3:7\].
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