Question

The joint equation of pair of lines having inclinations 60° and 120°and passing through the origin is ______.

Options

• 3x² + y² = 0

• 3x² – y² = 0

• x² – 3y² = 0

• x² + 3y² = 0

Answer 1

The joint equation of pair of lines having inclinations 60° and 120°and passing through the origin is 3x² – y² = 0.

Explanation:

Slopes of the lines are m₁ = tan 60° = `sqrt(3)x` and m₂ = tan 120° = `- sqrt(3)`

Equations of lines are y = `sqrt(3)`x and y = `- sqrt(3)x`

∴ The joint equation of the pair of lines is

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

⇒ 3x² – y² = 0