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

Options

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

Answer

A

Explanation

Since, lines passing through the origin and trisecting the frist quadrant therefore there slopes are
`m_(1)=tan30^(@),m_(2)=tan60^(@)`
`impliesm_(1)=(1)/(sqrt(3)),m_(2)=sqrt(3)`
`therefore`Required joint equation of the lines is
`(y-(1)/(sqrt(3))x)(y-sqrt(3)x)=0`
`implies(sqrt(3)y-x)(y-sqrt(3)x)=0`
`implies sqrt(3)y^(2)-3xy-xy+sqrt(3)x^(2)=0`
`implies sqrt(3)x^(2)-4xy+sqrt(3)y^(2)=0`
`implies sqrt(3)x^(2)-4xy+sqrt(3)y^(2)=0`