If the angle between the pair of straight lines represented by the equation `x^2-3xy+lambday^2+3x-5y+2=0` is `tan^(-1)(1//3)`, where `lambda` is non - negative real number , then `lambda` is equal to

Options

A. 2
B. 0
C. 3
D. 1

Answer

A

Explanation

Given equation is compared by the standard form, we get
`a=1,h=-3/2, b=lamda,g=3/2,f=-5/2, c=2`
Given that `theta=tan^(-1)(1/3)`
`implies1/3=tantheta=1/3=(2sqrt(((-3)/2)^(2)-lamda))/(lamda+1)`
`implies(lamda+1)^(2)=9(9-4lamda)`
`implieslamda^(2)+1+2lamda-81-36 lamda`
`implieslamda^(2)+38 lamda=80=0`
`=lamda=(-38)+-sqrt((38)^(2)+320)/2`
`=lamda=(-38+-42)/2`
`implieslamda=2`