A) 3/2
B) 3/10
C) 6
D) None of these
Correct Answer: B
Solution :
Here the lines are, \[3x+4y-9=0\] ......(i) and \[6x+8y-15=0\] ......(ii) Now distance from origin of both the lines are \[\frac{-9}{\sqrt{{{3}^{2}}+{{4}^{2}}}}=-\frac{9}{5}\]and \[\frac{-15}{\sqrt{{{6}^{2}}+{{8}^{2}}}}=-\frac{15}{10}\] Hence distance between both the lines are \[\,\left| \,-\frac{9}{5}-\left( -\frac{15}{10} \right)\, \right|\,=\frac{3}{10}\]. Ailter: Put \[y=0\] in the first equation, we get \[x=3\]therefore, the point (3, 0) lies on it. So the required distance between these two lines is the perpendicular length of the line \[6x+8y=15\] from the point (3, 0). i.e., \[\frac{6\times 3-15}{\sqrt{{{6}^{2}}+{{8}^{2}}}}=\frac{3}{10}\].
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