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)-2sqrt(2)xy+y^(2)=0`
B. `x^(2)-2sqrt(2)xy-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+sqrt(2)) and m_(2)=(1)/(1+sqrt(2))=sqrt(2)-1`
`implies[y-(1+sqrt(2))x][y-(sqrt(2)-1)x]=0`
`impliesy^(2)-(sqrt(2)-1)xy-(1+sqrt(2))xy+(2-1)x^(2)=0`
`impliesy^(2)-(sqrt(2)-1+1+sqrt(2))xy+x^(2)=0`
`impliesy^(2)-2sqrt(2)xy+x^(2)=0`