A) \[\sqrt{5}\]
B) \[\frac{2}{\sqrt{5}}\]
C) \[\frac{1}{\sqrt{5}}\]
D) \[\frac{\sqrt{5}}{2}\]
E) \[\sqrt{\frac{5}{2}}\]
Correct Answer: A
Solution :
\[\because \]The given equation of pair of parallel lines is \[{{x}^{2}}+4xy+4{{y}^{2}}+3x+6y-4=0\] Here, \[a=1,b=4g=\frac{3}{2}\]and \[c=-4.\] Then, required distance\[=2\sqrt{\frac{{{g}^{2}}-ac}{a(a+b)}}\] \[=2\sqrt{\frac{\frac{9}{4}+4}{5}}=\frac{2.\sqrt{16+9}}{2.\sqrt{5}}\] \[=\frac{2\sqrt{25}}{2\sqrt{5}}=\frac{5}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}\] \[=\sqrt{5}\]
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