A) \[\frac{2}{5}\]
B) \[\frac{12}{5}\]
C) \[\frac{5}{12}\]
D) \[\frac{3}{5}\]
Correct Answer: B
Solution :
\[{{d}_{1}}=\] distance of perpendicular from \[(0,\,0)\] to \[3x+4y+7=0\] \[{{d}_{1}}=\frac{3\times 0+4\times 0+7}{\sqrt{{{3}^{2}}+{{4}^{2}}}}=\frac{7}{5}\] \[{{d}_{2}}=\frac{3\times 0+4\times 0+(-5)}{\sqrt{{{3}^{2}}+{{4}^{2}}}}=\frac{-5}{5}\] \ Required distance \[=\left| \,{{d}_{1}}-{{d}_{2}} \right|\]\[=\left| \,\frac{7}{5}-\left( \frac{-5}{5} \right)\, \right|=\frac{12}{5}.\]
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