The joint equation of pair of straight lines passing through origin and having slopes `(1+sqrt(2)) and ((1)/(1+sqrt(2)))` is

Options

A. `x^(2)-2sqrt2xy+y^(2)=0`
B. `x^(2)-2sqrt2xy-y^(2)=0`
C. `x^(2)+2xy-y^(2)=0`
D. `x^(2)+2xy+y^(2)=0`

Answer

A

Explanation

Required equation of pair of straight lines passing through origin and having slopes,
`m_(1)=(1+sqrt2)` and `m_(2)=1/(1+sqrt2)=sqrt-1`
`rArr[y-(1+sqrt2)x][y-(sqrt2-1)x]=0`
`rArry^(2)-(sqrt2-1)xy-(1+sqrt2)xy+(2-1)x^(2)=0`
`rArry^(2)-(sqrt2-1+1+sqrt2)xy+x^(2)=0`
`rArry^(2)-2sqrt2xy+x^(2)=0`