The length of the perpendicular from the origin to the line is 7 and the line makes the angle of - Maths - Straight Lines

Question

The length of the perpendicular from the origin to the line is 7
and the line makes the angle of 150o with the positive
direction of y-axis Then find the equation of the line

Rajat Sethi · Accepted Answer

Angle made with positive y-axis =150°∴Angle made with positive x-axis =60° and 180°-60°=120°Let intercepts made by the line on x and y axis be a and b respectively
,i,eCoordinates are A(a,0) and B(0,b)Slope=tan 120°    and  Slope=tan 60° ⇒b-00-a=-3        ⇒b-00-a=3⇒b=a3
(i)       ⇒b=-a3
(ii)equation of line:y-0=b-00-a(x-a)⇒y=-3(x-a)      and y=3(x-a)⇒3x+y-a3=0 and 3x-y-a3=0Now,dorigin=7⇒Ax+By+cA2+B2=7⇒3
0±1
0-a33+1=7⇒a3=±14∴equation of lines are:3x+y±14=0 and 3x-y±14=0<img alt=""
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The length of the perpendicular from the origin to the line is 7 and the line makes the angle of 150o with the positive direction of y-axis. Then find the equation of the line.

The length of the perpendicular from the origin to the line is 7 and the line makes the angle of 150^o with the positive direction of y-axis. Then find the equation of the line.