Answer 1

Let OA and OB be the lines through the origin making an angle of 60° with the line y = 3.

∴ OA and OB make an angle of 60° and 120° with the positive direction of the X-axis.

∴ slope of OA = tan 60° = `sqrt3`

∴ equation of the line OA is

y = `sqrt3`x i.e. `sqrt3`x - y = 0

Slope of OB = tan 120° = tan (180° - 60°)

= - tan 60° = - `sqrt3`

∴ equation of the line OB is

y = - `sqrt3`x, i.e. `sqrt3`x + y = 0

∴ required joint equation of the lines is

`(sqrt3"x" - "y")(sqrt3"x" + "y") = 0`

i.e. 3x² - y² = 0