question_answer

If the straight line through the point P (3, 4) makes an angle \[\frac{\pi }{6}\] with x-axis and meets the line \[~12x+5y+10=0\] at Q, find the length of PQ.

A)  \[\frac{132}{12\,\sqrt{3}+5}\]  

B)  \[\frac{123}{8\,\sqrt{3}+7}\]

C)  \[\frac{115}{6\,\sqrt{2}+5}\]                

D)  \[\frac{110}{4\,\sqrt{2}+7}\]

E)  None of these