A) \[\frac{3}{2}\]
B) \[\frac{3}{4}\]
C) \[\frac{1}{10}\]
D) \[\frac{1}{20}\]
Correct Answer: B
Solution :
Since, given lines are parallel. Thus, diameter of the circle is the distance between the tangents\[3x-4y+4=0\]and \[3x-4y-\frac{7}{2}=0\]Since, these lines are in opposite direction. Thus, distance between these lines \[=\frac{4}{\sqrt{9+16}}+\frac{7/2}{\sqrt{9+16}}\] \[=\frac{4}{5}+\frac{7}{10}=\frac{15}{10}=\frac{3}{2}\] Hence, radius\[=\frac{1}{2}\](length of diameter) \[=\frac{1}{2}\left( \frac{3}{2} \right)=\frac{3}{4}\]
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