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

Options

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

Answer

A

Explanation

It is given that slopes of thelines passing through origin are
`m_(1)("let")=(1+sqrt(2)) and m_(2)("let")=(-1)/(1+sqrt(2))=-(sqrt(2)-1)`
`therefore`Required joint equation of lines passing through origin is
`[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)-2xy-x^(2)=0impliesx^(2)+2xy-y^(2)=0`