The lines represented by `x^(2)+2lambda xy+2y^(2)=0` and the lines represented by `1+lambda_x^(2)-8xy+y^(2)=0` are equally inclined, then

Options

A. `lambda ` is any real number
B. `lambda gt 2`
C. `lambda = +-2`
D. `lambda lt -2`

Answer

C

Explanation

If the lines given by the two equations are equally inclined , then they the same bisectors. Therefore, equations `(x^2-y^2)/(1-2)=(xy)/(lambda) and (x^2-y^2)/(1+lambda-1)=(xy)/(-4)` represent the same pair of lines.
`rArr lambda x^2+xy-lambday^2=0 and 4x^2+lambda xy-4y^2=0` represent the same pair of lines.
`therefore (lambda)/(4)=(1)/(lambda)=(-lambda)/(-4)`
`rArr lambda^2=4rArr =+-2` .