The length of the perpendicular from the origin to a line is 7, and the line makes an angle of 150 0 with the positive direction of y–axis. Find the equation of the line.

Question

Philoid · Accepted Answer

Assuming:

AB be the given line which makes an angle of 150⁰ with the positive direction of y–axis and OQ be the perpendicular drawn from the origin on the line.

Given:

p = 7 and α = 30°

Explanation:

So, the equation of the line AB is

Formula Used: x cos α + y sin α = p

⇒ x cos 30° + y sin 30° = 7

⇒

⇒ √3 x + y = 14

Hence, the equation of line in normal form is √3 x + y = 14

The length of the perpendicular from the origin to a line is 7, and the line makes an angle of 1500 with the positive direction of y–axis. Find the equation of the line.

The length of the perpendicular from the origin to a line is 7, and the line makes an angle of 150⁰ with the positive direction of y–axis. Find the equation of the line.