Question

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
A. `lambda` is any real number
B. `lambda gt 2`
C. `lambda = pm2`
D. `lambda lt -2`

Answer 1

Correct Answer - C
If the lines given by the two equations are equally inclined then they have 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" "lambdax^(2)+xy-lambday^(2)=0 and 4x^(2)+lambdaxy-4y^(2)=0`,
represent the same pair of lines
`therefore" "(lambda)/(4)=(1)/(lambda)=(-lambda)/(-4)rArr lambda^(2)=4 rArr lambda= pm 2`