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The joint equation of lines passing thro...

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

A

`x^2+sqrt(3)xy-y^2=0`

B

`x^2-sqrt(3)xy-y^2=0`

C

`sqrt(3)x^2-4xy+sqrt(3)y^2=0`

D

`3x^2-y^2=0`

Text Solution

Verified by Experts

The correct Answer is:
C
In a trisection of lines in quadrant , angle `90^@` is divided into three parts and each part contain `30^@`.
`therefore` Equation of line AB is `y=tan30^(@) x rArr y=(1)/(sqrt(3))x`
`x-sqrt(3)y=0`
And equation of line AC is `y=tan60^@ x rArr y=sqrt(3)x`
`(sqrt(3)x-y)=0`
`therefore` Combined equation is `(x-sqrt(3)y)(sqrt(3)x-y=0`
`rArr sqrt(3)x^2-xy-3xy+sqrt(3)y^2=0`
`rArr sqrt(3)x^2-4xy+sqrt(3)y^2=0`
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Knowledge Check

  • The joint equation of lines passing through the origin and trisecting the second and fourth quadrant is

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

  • The joint equation of lines passing through the origin and bisecting the angles between co-ordinate axes is

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

  • D.E. of lines, passing through the origin, is

    A
    `xy_(1)=y`
    B
    `xy=y_(1)`
    C
    `xy+y_(1)=0`
    D
    None of these

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