Question

Find the equation of the lines passing through the point (1, 1) and the perpendicular from the origin makes an angle 60° with x-axis

Answer 1

The equation of the line in the normal form is x cos α + y sin α = p  ......(1)

Given α = 60°

∴ cos 60° = `1/2`, sin 60° = `sqrt(3)/2`

(1) ⇒ `x * 1/2 +y * sqrt(3)/2` = p

`x + sqrt(3)` = 2p  .......(2)

This line passes through the point (1, 1)

∴ `1 + sqrt(3)` = 2p

Substituting for p in equation (2)

The required equation is `x + sqrt(3)y = 1 + sqrt(3)`