Question

The length of the perpendicular from the origin to a line is 7 and the line makes an angle of 150 degrees with the positive direction of the y-axis. Then the equation of line is​

Answer 1

Given,

angle made with the positive y-axis=150°

∴ Angle made with positive x-axis=60° and 180° − 60° = 120°

Let intercepts made by the line on x & y axis be a & b respectively.

∴ Co-ordinates are A(0,0) & B(0,b).

∴Slope=tan120

$= \frac{b - 0}{0 - a} = \sqrt{3}$

$= b = + \sqrt{3} a$

or,

Slope = tan 60°

$= \frac{b - 0}{0 - a} = \sqrt{3}$

$= b = - \sqrt{3}a$

Equation of the lines will be:-

$y - 0 = \frac{b}{ - a} (x - a)$

$y = \sqrt{3} (x - a)$

Also given, that the distance from origin is 7 units.

$d_{origin} = 7$