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

Options

A. `x^(2)+sqrt3xy-y^(2)=0`
B. `x^(2)-sqrt3xy-y^(2)=0`
C. `sqrt3x^(2)-4xy+sqrt3y^(2)=0`
D. `3x^(2)-y^(2)=0`

Answer

C

Explanation

In a trisection of lines in quadrant, angle `90^(@)` is divided into three parts and each part contain `30^(@)`
`therefore` Equation of line OB is

`y=tan 30^(@) x Rightarrow y=(1)/(sqrt3)x`
And equation of line OC is
`y=tan 60^(@)x Rightarrow y=sqrt3x`
`(sqrt3x-y)=0`
`therefore` Combined equation is
`(x-sqrt3y)(sqrt3x-y)=0`
`Rightarrow sqrt3x^(2)-xy-3xy+sqrt3y^(2)=0`
`Rightarrow sqrt3x^(2)-4xy+sqrt3y^(2)=0`