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

Options

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

Answer

A

Explanation

Since , lines passing throught the orgin and trisecting the first quadrant therefore there slopes are
`m_(1) =tan 30^(@) , m_(2) = tan 60^(@)`
`rArr" "m_(1) =(1)/(sqrt(3)) ,m_(2) = sqrt(3)`
`therefore` Required joint equation of the lines is
`(y -(1)/(sqrt(3))x) (y--sqrt(3x)) = 0`
`rArr " "(sqrt(3y) -x) (y - sqrt(3)x)=0`
`rArr " " sqrt(3)x^(2) - 4xy + sqrt(3)y^(2) = 0`