The equation x^2-5 x y+p y^2+3 x-8 y+2=0 represents a pair of straight lines. If is the angle between them, then is equal to

Step-by-step solution

Comparing the given equation x^2-5 x y+p y^2+3 x-8 y+2=0 with a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 we get a=1, h= -5 2 , b=p, g= 3 2 , f=-4 and c=2 Eq. (i) represents a pair of straight lines, if array cc & a b c+2 f g h-a f^2-b g^2-c h^2=0 & 1 p 2+2 (-4) 3 2 ( -5 2 )-1 (-4)^2 & -p ( 3 2 )^2-2 ( -5 2 )^2=0 & p=6 p=6 array Required angle, = 2 h^2-a b a+b = 2 ( -5 2 )^2-1 6 1+6 array cc & = 1 7 = ⁻¹ 1 7 & = 1 50 array