question_answer

The length of the perpendicular from the origin to a line is 7 and line makes an angle of \[150{}^\circ \] with the positive direction of y-axis, then the equation of the line is

A) \[\sqrt{3}x+y=7\]

B) \[\sqrt{3}x-y=14\]

C) \[\sqrt{3}x+y+14=0\]

D) \[\sqrt{3}x+y-14=0\]

Correct Answer: D

Solution :

[d] Here p=7 and \[\alpha =30{}^\circ \] \[\therefore \] Equation of the required line is \[x\cos 30{}^\circ +y\sin 30{}^\circ =7\] or \[x\frac{\sqrt{3}}{2}+y\times \frac{1}{2}=7\] or \[\sqrt{3}x+y=14\]