A) \[\frac{7\sqrt{7}}{2\sqrt{3}}\]
B) \[\frac{5\sqrt{7}}{2\sqrt{3}}\]
C) \[\frac{14\sqrt{7}}{\sqrt{3}}\]
D) \[\frac{7\sqrt{7}}{5\sqrt{3}}\]
Correct Answer: B
Solution :
\[|\,\sqrt{3}\,(1-2z)+2i\,|\,=2\sqrt{7}\] is the equation of circle having centre is \[\left( \frac{1}{2},\frac{1}{\sqrt{3}} \right)\] and having radius\[\frac{\sqrt{7}}{3}\]. Also, \[\left| \,\sqrt{3}(1-2z)-2i \right|=\left| \sqrt{3}(9-z)+18i \right|\] Is the equation of perpendicular bisector of line joining \[\left( -1,\frac{-2}{\sqrt{3}} \right)\] and \[\left( 9,6\sqrt{3} \right)\] So, \[MQ=\sqrt{{{\left( 4-\frac{1}{2} \right)}^{2}}+{{\left( \frac{8}{\sqrt{3}}-\frac{1}{\sqrt{3}} \right)}^{2}}}=\frac{7\sqrt{7}}{2\sqrt{3}}\] \[\therefore \]Required distance \[=(MQ)-\] (radius) \[=\frac{7\sqrt{7}}{2\sqrt{3}}-\sqrt{\frac{7}{3}}=\frac{5}{2}\sqrt{\frac{7}{3}}\]You need to login to perform this action.
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