Question

The joint equation of the lines passing through the origin and trisecting the first quadrant is ______.

Options

• `sqrt3x^2 - 4"xy" + sqrt3 "y"^2 = 0`

• `x^2 + sqrt3"xy" - "y"^2 = 0`

• `3x^2 - "y"^2 = 0`

• `x^2 - sqrt3"xy" - "y"^2 = 0`

Answer 1

The joint equation of the lines passing through the origin and trisecting the first quadrant is `underlinebb(sqrt3x^2 - 4"xy" + sqrt3 "y"^2 = 0)`.

Explanation:

Since, lines passing through the origin and trisecting the first quadrant therefore there slopes are

m₁ = tan 30°, m₂ = tan 60°

`=> "m"_1 = 1/sqrt3, "m"_2 = sqrt3`

∴ Required joint equation of the lines is

`("y" - 1/sqrt3 x)("y" - sqrt3 x)` = 0

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

`=> sqrt3"y"^2 - 3"xy" - "xy" + sqrt3x^2` = 0

`=> sqrt3x^2 - 4"xy" + sqrt3"y"^2` = 0