Any line through P(3,4) making an angle π6 with x−axis is
x−3cos30o=y−4sin30o=r
Where r represents the distance of any point on this line from the given point P(3,4)
Any point Q on it is (r√3/2)+3,(r/2)+4 and Q lies on 12x+5y+10=0
∴12[(r√32)+3]+5(r2+4)+10=0
∴(12√3+5)r+132=0
∴r=|−132|12√(3)+5=13212√(3)+5.