If the angles between the pair of straight lines represented by the equation x^2-3 x y+ y^2+3 x-5 y+2=0 is ⁻¹ 1 3 . Where is a non-negative real number, then is

Step-by-step solution

Let be the angle between the given pair of straight lines x^2-3 x y+ y^2+3 x-5 y+2=0 ...(i) = ⁻¹ 1 3 (given) or = 1 3 We know that, = 2 h^2-a b a+b ...(ii) where, h=- 3 2 , a=1, b= put these value in Eq. (ii), we get aligned 1 3 & = 2 9 4 - 1 1+ (1+ ) & =3 9-4 aligned On squaring both sides, we get aligned (1+ )^2 & =(3 9-4 )^2 1+ ^2+2 & =81-36 aligned array rr & ^2+38 -80=0 & ^2+40 -2 -80=0 & ( +40)-2( +40)=0 & ( -2)( +40)=0 & =2,-40 =2 array ( ^ ' is non-negative real number)