The pair equation of the lines passing through the origin and having slopes 3 and `-(1)/(3)`, is

Options

A. `3y^2+8xy-3x^2=0`
B. `3x^2+8xy-3y^2=0`
C. `3y^2-8xy+3x^2=0`
D. `3x^2+8xy+3y^2=0`

Answer

B

Explanation

We know that , equation of line passing through origin having slope m is `y=mx`
`therefore` Equation of line passing through origin and having slope 3 and `-(1)/(3)` are `y=3x`.
and `y=-(1)/(3)x`
Now , combined equation of lines is `(y-3x)(y+(1)/(3)x)=0`
`rArr y^2+(xy)/(3)-3xy-x^2=0`
`rArr 3y^2+xy-9xy-3x^2=0`
`rArr 3y^2-8xy-3x^2=0`
`therefore 3x^2+8y-3y^2=0`