Question

The joint equation of pair of lines through the origin, each of which makes an angle of 60° with Y-axis, is ______ 

Options

• x² - 3y² = 0

• x² + 3y² = 0

• 3x² - y² = 0

• 3x² + y² = 0

Answer 1

The joint equation of pair of lines through the origin, each of which makes an angle of 60° with Y-axis, is x² - 3y² = 0

Explanation:

Let OA and OB be the required lines.

∴ angles made by OA and OB with X-axis are 30° and 150° respectively.

∴ their equations are y = `1/sqrt3x` and y = `-1/sqrt3x`

i.e., `x - sqrt3y = 0  "and"  x + sqrt3y = 0`

∴ The joint equation of the lines is

`(x - sqrt3y)(x + sqrt3y) = 0 ⇒ x^2 - 3y^2 = 0`