Question

A straight line L through the point (3, –2) is inclined at an angle of 60° to the line `sqrt(3)x + y` = 1. If L also intersects the x-axis, then the equation of L is ______.

Options

• `y + sqrt(3)x + 2 - 3sqrt(3)` = 0

• `sqrt(3)y + x - 3 + 2sqrt(3)` = 0

• `y - sqrt(3)x + 2 + 3sqrt(3)` = 0

• `sqrt(3)y - x + 3 + 2sqrt(3)` = 0

Answer 1

A straight line L through the point (3, –2) is inclined at an angle of 60° to the line `sqrt(3)x + y` = 1. If L also intersects the x-axis, then the equation of L is `underlinebb(y - sqrt(3)x + 2 + 3sqrt(3) = 0)`.

Explanation:

Given equation of line is `y + sqrt(3)x - 1` = 0

⇒ y = `-sqrt(3)x + 1`

⇒ (Slope)m₂ = `-sqrt(3)`

Let the other slope be m₁

∴ tan 60° = `|(m_1 - (-sqrt(3)))/(1 + (-sqrt(3)m_1))|`

⇒ m₁ = 0, m₂ = `sqrt(3)`

Since line L is passing through (3, –2)

∴ y – (–2) = `+ sqrt(3)(x - 3)`

⇒ y + 2 = `sqrt(3)(x - 3)`

`y - sqrt(3)x + 2 + 3sqrt(3)` = 0