A) \[\frac{3}{2\sqrt{13}}\]
B) \[\frac{3}{4\sqrt{13}}\]
C) \[\frac{3}{8\sqrt{13}}\]
D) \[2\]
Correct Answer: B
Solution :
Given, straight lines are \[2x-3y+1=0\] and \[4x-6y+5=0\] or \[2x-3y+\frac{5}{2}=0\] Which re parallel. Since, these lines are the tangents of a circle, therefore distance d between these lines is the diameter of the circle. \[\therefore \] \[d=\left| \frac{\frac{5}{2}-1}{\sqrt{4+9}} \right|=\frac{3}{2\sqrt{13}}\] \[\therefore \] Radius of the circle is\[\frac{3}{4\sqrt{13}}\].
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