A) \[\frac{3}{2}\]
B) \[\frac{3}{10}\]
C) \[6\]
D) None of these
Correct Answer: B
Solution :
Key Idea If coefficient of \[x\] and \[y\] of both the lines are same, then the lines are parallel Given, equation of lines are \[3x+4y=9\] ... (i) and \[6x+8y=15\] \[\Rightarrow \] \[3x+4y=\frac{15}{2}\] ... (ii) \[\therefore \]Both lines are parallel, therefore the distance between two lines \[=\frac{\left| \frac{15}{2}-9 \right|}{\sqrt{{{3}^{2}}+{{4}^{2}}}}\] \[=\frac{|15-18|}{2\sqrt{25}}\] \[=\frac{3}{2\cdot 5}=\frac{3}{10}\] Alternative The perpendicular distance from origin to the line \[{{L}_{1}}\] is \[{{d}_{1}}=\frac{9}{\sqrt{{{3}^{2}}+{{4}^{2}}}}=\frac{9}{5}\] and \[{{d}_{2}}=\frac{\frac{15}{2}}{\sqrt{{{3}^{2}}+{{4}^{2}}}}\] \[=\frac{15}{2\cdot 5}=\frac{15}{10}\] \[\therefore \]Distance between \[{{L}_{1}}\] and \[{{L}_{2}}\] is \[d={{d}_{1}}-{{d}_{2}}\] \[=\frac{9}{5}-\frac{15}{10}=\frac{18-15}{10}\] \[=\frac{3}{10}\]You need to login to perform this action.
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